Details

analyze449.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
37.4%	62.4%	0.1%	6
49.9%	49.9%	0.1%	7
62.4%	37.4%	0.1%	8
62.4%	37.4%	0.1%	9
71.8%	28.1%	0.1%	10
79.6%	20.3%	0.1%	11
79.6%	20.3%	0.1%	12
85%	14.8%	0.1%	13
89.3%	10.5%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample49.0ms (0.1%)

Algorithm

1×

intervals

Results

21.0ms	66×	body	1024	valid
9.0ms	144×	body	128	valid
7.0ms	33×	body	512	valid
2.0ms	13×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify101.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	159	14
1	159	14

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 1

Compiler

Compiled 9 to 8 computations (11.1% saved)

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 z (sin.f64 y))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_8284`
7×	`pow1_binary64_8323` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
6×	`associate-l_binary64_8203` `associate-r_binary64_8202`
5×	`add-log-exp_binary64_8301`
2×	`prod-exp_binary64_8311` `unswap-sqr_binary64_8230` `cbrt-unprod_binary64_8295` `pow-prod-down_binary64_8333` `*-commutative_binary64_8193`
1×	`flip3--_binary64_8266` `diff-log_binary64_8354` `sub-neg_binary64_8255` `flip--_binary64_8237` `cancel-sign-sub-inv_binary64_8228`

Counts

3 → 48

Calls

6 calls:

5.0ms	(*.f64 z (sin.f64 y))
4.0ms	(*.f64 x (cos.f64 y))
4.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.0ms	(*.f64 x (cos.f64 y))

series367.0ms (1.1%)

Counts

3 → 32

Calls

3 calls:

230.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
72.0ms	(*.f64 z (sin.f64 y))
65.0ms	(*.f64 x (cos.f64 y))

Compiler

Compiled 484 to 435 computations (10.1% saved)

simplify69.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4937	874
1	4937	874

prune197.0ms (0.6%)

Pruning

36 alts after pruning (35 fresh and 1 done)

	Pruned	Kept	Total
New	45	35	80
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	45	36	81

Error

0.0b

Counts

81 → 36

Compiler

Compiled 1145 to 509 computations (55.5% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(+.f64 (.f64 x (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
0.0b	(+.f64 (.f64 x (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 z (sin.f64 y))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_8284`
7×	`pow1_binary64_8323` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `add-log-exp_binary64_8301` `add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
6×	`associate-l_binary64_8203` `associate-r_binary64_8202`
2×	`prod-exp_binary64_8311` `unswap-sqr_binary64_8230` `cbrt-unprod_binary64_8295` `pow-prod-down_binary64_8333` `sum-log_binary64_8353` `*-commutative_binary64_8193`
1×	`flip-+_binary64_8236` `flip3-+_binary64_8265` `associate-+r-_binary64_8196` `+-commutative_binary64_8192` `unsub-neg_binary64_8256` `neg-sub0_binary64_8257` `neg-log_binary64_8355`

Counts

3 → 50

Calls

6 calls:

5.0ms	(+.f64 (.f64 x (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(*.f64 x (cos.f64 y))
0.0ms	(+.f64 (.f64 x (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
0.0ms	(*.f64 x (cos.f64 y))

series368.0ms (1.1%)

Counts

3 → 32

Calls

3 calls:

230.0ms	(+.f64 (.f64 x (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
69.0ms	(*.f64 z (sin.f64 y))
68.0ms	(*.f64 x (cos.f64 y))

Compiler

Compiled 510 to 461 computations (9.6% saved)

simplify85.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4896	880
1	4896	880

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 x (*.f64 z y))
0.0b	(-.f64 x (*.f64 z y))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_8301`
1×	`pow1_binary64_8323` `flip3--_binary64_8266` `add-sqr-sqrt_binary64_8284` `diff-log_binary64_8354` `sub-neg_binary64_8255` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `flip--_binary64_8237` `add-cube-cbrt_binary64_8297` `cancel-sign-sub-inv_binary64_8228` `*-un-lft-identity_binary64_8262`

Counts

1 → 12

Calls

2 calls:

3.0ms	(-.f64 x (*.f64 z y))
0.0ms	(-.f64 x (*.f64 z y))

series80.0ms (0.2%)

Counts

1 → 18

Calls

1 calls:

80.0ms

(-.f64 x (*.f64 z y))

Compiler

Compiled 119 to 132 computations (-10.9% saved)

simplify101.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5423	248

localize10.0ms (0%)

Local error

Found 6 expressions with local error:

0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.0b	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 z (sin.f64 y))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_8284`
7×	`pow1_binary64_8323` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
6×	`associate-l_binary64_8203` `associate-r_binary64_8202`
5×	`add-log-exp_binary64_8301`
2×	`prod-exp_binary64_8311` `unswap-sqr_binary64_8230` `cbrt-unprod_binary64_8295` `pow-prod-down_binary64_8333` `*-commutative_binary64_8193`
1×	`flip3--_binary64_8266` `diff-log_binary64_8354` `sub-neg_binary64_8255` `flip--_binary64_8237` `cancel-sign-sub-inv_binary64_8228`

Counts

3 → 48

Calls

6 calls:

5.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (*.f64 z (sin.f64 y)))
4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(*.f64 x (cos.f64 y))
0.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.0ms	(*.f64 x (cos.f64 y))

series364.0ms (1.1%)

Counts

3 → 32

Calls

3 calls:

222.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (*.f64 z (sin.f64 y)))
72.0ms	(*.f64 x (cos.f64 y))
69.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 536 to 487 computations (9.1% saved)

simplify71.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5487	874

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (*.f64 z (sin.f64 y)) 3)
0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 z (sin.f64 y))
0.2b	(pow.f64 (*.f64 z (sin.f64 y)) 3)
33.7b	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_8284`
11×	`pow1_binary64_8323` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298`
10×	`add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
8×	`cbrt-prod_binary64_8293`
6×	`associate-l_binary64_8203` `associate-r_binary64_8202`
4×	`add-log-exp_binary64_8301`
3×	`pow-unpow_binary64_8339` `prod-exp_binary64_8311` `cbrt-unprod_binary64_8295` `pow-prod-down_binary64_8333`
2×	`cube-mult_binary64_8292` `unpow3_binary64_8328` `unswap-sqr_binary64_8230` `cube-prod_binary64_8290` `unpow-prod-down_binary64_8341` `pow-exp_binary64_8330` `sqr-pow_binary64_8234` `*-commutative_binary64_8193` `rem-cube-cbrt_binary64_8285` `pow-pow_binary64_8334`
1×	`rem-cbrt-cube_binary64_8286` `pow1/3_binary64_8344` `pow-to-exp_binary64_8331`

Counts

4 → 75

Calls

8 calls:

4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
4.0ms	(pow.f64 (*.f64 z (sin.f64 y)) 3)
4.0ms	(*.f64 x (cos.f64 y))
0.0ms	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))

series354.0ms (1.1%)

Counts

4 → 28

Calls

4 calls:

140.0ms	(pow.f64 (*.f64 z (sin.f64 y)) 3)
76.0ms	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
70.0ms	(*.f64 x (cos.f64 y))
67.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 705 to 632 computations (10.4% saved)

simplify58.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4952	906
1	4952	906

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cos.f64 y) (cbrt.f64 x)))
0.2b	(*.f64 (cos.f64 y) (cbrt.f64 x))
0.1b	(*.f64 z (sin.f64 y))
0.0b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cos.f64 y) (cbrt.f64 x))) (.f64 z (sin.f64 y)))
0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_8293`
23×	`add-sqr-sqrt_binary64_8284`
15×	`add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
11×	`pow1_binary64_8323`
9×	`pow1/3_binary64_8344`
6×	`add-exp-log_binary64_8300` `associate-l_binary64_8203` `associate-r_binary64_8202` `swap-sqr_binary64_8229`
4×	`unswap-sqr_binary64_8230` `add-cbrt-cube_binary64_8298` `add-log-exp_binary64_8301`
2×	`pow-sqr_binary64_8235` `pow-prod-up_binary64_8332` `pow-prod-down_binary64_8333`
1×	`prod-exp_binary64_8311` `pow2_binary64_8343` `cbrt-unprod_binary64_8295` `*-commutative_binary64_8193` `pow-plus_binary64_8325`

Counts

4 → 73

Calls

8 calls:

9.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cos.f64 y) (cbrt.f64 x))) (.f64 z (sin.f64 y)))

series316.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
79.0ms	(cbrt.f64 x)
76.0ms	(cbrt.f64 x)
71.0ms	(cbrt.f64 x)

Compiler

Compiled 442 to 358 computations (19% saved)

simplify80.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune2.6s (7.7%)

Pruning

140 alts after pruning (134 fresh and 6 done)

	Pruned	Kept	Total
New	276	104	380
Fresh	0	30	30
Picked	0	0	0
Done	0	6	6
Total	276	140	416

Error

0.0b

Counts

416 → 140

Compiler

Compiled 5502 to 2523 computations (54.1% saved)

localize11.0ms (0%)

Local error

Found 6 expressions with local error:

0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (pow.f64 (*.f64 z (sin.f64 y)) 1))
0.0b	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (pow.f64 (*.f64 z (sin.f64 y)) 1))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 z (sin.f64 y))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_8284`
9×	`*-un-lft-identity_binary64_8262`
8×	`add-cube-cbrt_binary64_8297`
7×	`pow1_binary64_8323` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298`
6×	`associate-l_binary64_8203` `associate-r_binary64_8202`
5×	`add-log-exp_binary64_8301` `cancel-sign-sub-inv_binary64_8228`
2×	`prod-exp_binary64_8311` `unswap-sqr_binary64_8230` `cbrt-unprod_binary64_8295` `pow-prod-down_binary64_8333` `*-commutative_binary64_8193`
1×	`flip3--_binary64_8266` `diff-log_binary64_8354` `sub-neg_binary64_8255` `distribute-lft-out--_binary64_8214` `unpow-prod-down_binary64_8341` `sqr-pow_binary64_8234` `flip--_binary64_8237`

Counts

3 → 53

Calls

6 calls:

9.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (pow.f64 (*.f64 z (sin.f64 y)) 1))
4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(*.f64 x (cos.f64 y))
0.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (pow.f64 (*.f64 z (sin.f64 y)) 1))
0.0ms	(*.f64 x (cos.f64 y))

series373.0ms (1.1%)

Counts

3 → 32

Calls

3 calls:

231.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (pow.f64 (*.f64 z (sin.f64 y)) 1))
72.0ms	(*.f64 z (sin.f64 y))
70.0ms	(*.f64 x (cos.f64 y))

Compiler

Compiled 588 to 539 computations (8.3% saved)

simplify84.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4918	910
1	4918	910

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

3.0b	(exp.f64 (log.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))
0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 z (sin.f64 y))
3.0b	(exp.f64 (log.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_8284`
10×	`add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
9×	`pow1_binary64_8323`
8×	`add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298`
6×	`associate-l_binary64_8203` `associate-r_binary64_8202` `add-log-exp_binary64_8301`
4×	`exp-prod_binary64_8314`
3×	`exp-sum_binary64_8308` `log-prod_binary64_8348`
2×	`prod-exp_binary64_8311` `log-div_binary64_8349` `flip3--_binary64_8266` `unswap-sqr_binary64_8230` `cbrt-unprod_binary64_8295` `pow-prod-down_binary64_8333` `exp-diff_binary64_8310` `flip--_binary64_8237` `*-commutative_binary64_8193`
1×	`diff-log_binary64_8354` `sub-neg_binary64_8255` `log-pow_binary64_8351` `cancel-sign-sub-inv_binary64_8228` `rem-exp-log_binary64_8302`

Counts

4 → 65

Calls

8 calls:

7.0ms	(exp.f64 (log.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))
4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(*.f64 x (cos.f64 y))
4.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

series1.5s (4.4%)

Counts

4 → 51

Calls

4 calls:

1.1s	(exp.f64 (log.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))
227.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
69.0ms	(*.f64 x (cos.f64 y))
67.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 1127 to 936 computations (16.9% saved)

simplify65.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4974	1543
1	4974	1543

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))))
0.1b	(*.f64 z (sin.f64 y))
0.2b	(.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y))))
6.5b	(sqrt.f64 (*.f64 z (sin.f64 y)))
6.5b	(sqrt.f64 (*.f64 z (sin.f64 y)))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1_binary64_8323`
32×	`sqrt-pow1_binary64_8280`
23×	`pow-prod-down_binary64_8333`
14×	`add-sqr-sqrt_binary64_8284`
12×	`pow1/2_binary64_8342`
10×	`pow-prod-up_binary64_8332` `add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
8×	`add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298`
7×	`associate-l_binary64_8203` `associate-r_binary64_8202`
6×	`pow-sqr_binary64_8235` `sqrt-prod_binary64_8278`
4×	`add-log-exp_binary64_8301` `swap-sqr_binary64_8229`
2×	`prod-exp_binary64_8311` `unswap-sqr_binary64_8230` `cbrt-unprod_binary64_8295` `*-commutative_binary64_8193`
1×	`pow2_binary64_8343` `sqrt-unprod_binary64_8282` `pow-plus_binary64_8325` `rem-square-sqrt_binary64_8274`

Counts

4 → 89

Calls

8 calls:

10.0ms	(.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y))))
4.0ms	(*.f64 z (sin.f64 y))
3.0ms	(sqrt.f64 (*.f64 z (sin.f64 y)))
3.0ms	(sqrt.f64 (*.f64 z (sin.f64 y)))
0.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))))

series246.0ms (0.7%)

Counts

4 → 26

Calls

4 calls:

68.0ms	(*.f64 z (sin.f64 y))
67.0ms	(.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y))))
58.0ms	(sqrt.f64 (*.f64 z (sin.f64 y)))
53.0ms	(sqrt.f64 (*.f64 z (sin.f64 y)))

Compiler

Compiled 862 to 632 computations (26.7% saved)

simplify75.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4973	832
1	4973	832

localize18.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 x (cos.f64 y))
0.0b	(sqrt.f64 (*.f64 x (cos.f64 y)))
0.0b	(sqrt.f64 (*.f64 x (cos.f64 y)))
0.0b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
0.1b	(*.f64 z (sin.f64 y))
0.2b	(pow.f64 (*.f64 z (sin.f64 y)) 3)
0.3b	(.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (*.f64 x (cos.f64 y))))
33.7b	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`pow1_binary64_8323`
28×	`sqrt-pow1_binary64_8280`
22×	`pow-prod-down_binary64_8333`
16×	`add-sqr-sqrt_binary64_8284`
12×	`add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
11×	`add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298`
10×	`pow-prod-up_binary64_8332` `pow1/2_binary64_8342`
8×	`cbrt-prod_binary64_8293`
7×	`associate-l_binary64_8203` `associate-r_binary64_8202`
6×	`pow-sqr_binary64_8235`
4×	`sqrt-prod_binary64_8278` `add-log-exp_binary64_8301` `swap-sqr_binary64_8229`
3×	`pow-unpow_binary64_8339` `prod-exp_binary64_8311` `cbrt-unprod_binary64_8295`
2×	`cube-mult_binary64_8292` `unpow3_binary64_8328` `unswap-sqr_binary64_8230` `cube-prod_binary64_8290` `unpow-prod-down_binary64_8341` `pow-exp_binary64_8330` `sqr-pow_binary64_8234` `*-commutative_binary64_8193` `rem-cube-cbrt_binary64_8285` `pow-pow_binary64_8334`
1×	`pow2_binary64_8343` `rem-cbrt-cube_binary64_8286` `pow1/3_binary64_8344` `sqrt-unprod_binary64_8282` `pow-plus_binary64_8325` `rem-square-sqrt_binary64_8274` `pow-to-exp_binary64_8331`

Counts

4 → 106

Calls

8 calls:

9.0ms	(.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (*.f64 x (cos.f64 y))))
4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(pow.f64 (*.f64 z (sin.f64 y)) 3)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
0.0ms	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))

series351.0ms (1%)

Counts

4 → 28

Calls

4 calls:

134.0ms	(pow.f64 (*.f64 z (sin.f64 y)) 3)
74.0ms	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
73.0ms	(.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (*.f64 x (cos.f64 y))))
69.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 999 to 729 computations (27% saved)

simplify63.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4938	1083
1	4938	1083

prune5.3s (15.6%)

Pruning

233 alts after pruning (222 fresh and 11 done)

	Pruned	Kept	Total
New	345	105	450
Fresh	12	117	129
Picked	0	0	0
Done	0	11	11
Total	357	233	590

Error

0.0b

Counts

590 → 233

Compiler

Compiled 8314 to 4028 computations (51.6% saved)

localize11.0ms (0%)

Local error

Found 6 expressions with local error:

0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (.f64 1 (.f64 z (sin.f64 y))))
0.0b	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (.f64 1 (.f64 z (sin.f64 y))))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 z (sin.f64 y))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_8284`
7×	`pow1_binary64_8323` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
6×	`associate-l_binary64_8203` `associate-r_binary64_8202`
5×	`add-log-exp_binary64_8301`
2×	`prod-exp_binary64_8311` `unswap-sqr_binary64_8230` `cbrt-unprod_binary64_8295` `pow-prod-down_binary64_8333` `*-commutative_binary64_8193`
1×	`flip3--_binary64_8266` `diff-log_binary64_8354` `sub-neg_binary64_8255` `distribute-lft-out--_binary64_8214` `flip--_binary64_8237` `cancel-sign-sub-inv_binary64_8228`

Counts

3 → 49

Calls

6 calls:

6.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (.f64 1 (.f64 z (sin.f64 y))))
4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(*.f64 x (cos.f64 y))
0.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (.f64 1 (.f64 z (sin.f64 y))))
0.0ms	(*.f64 x (cos.f64 y))

series358.0ms (1.1%)

Counts

3 → 32

Calls

3 calls:

221.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (.f64 1 (.f64 z (sin.f64 y))))
70.0ms	(*.f64 x (cos.f64 y))
67.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 588 to 539 computations (8.3% saved)

simplify71.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4937	888
1	4937	888

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (neg.f64 (*.f64 z y)))
0.0b	(+.f64 x (neg.f64 (*.f64 z y)))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-log-exp_binary64_8301`
3×	`*-un-lft-identity_binary64_8262`
2×	`sum-log_binary64_8353`
1×	`flip-+_binary64_8236` `flip3-+_binary64_8265` `pow1_binary64_8323` `associate-+r-_binary64_8196` `+-commutative_binary64_8192` `distribute-lft-out_binary64_8213` `add-sqr-sqrt_binary64_8284` `unsub-neg_binary64_8256` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `neg-sub0_binary64_8257` `add-cube-cbrt_binary64_8297` `neg-log_binary64_8355`

Counts

1 → 15

Calls

2 calls:

4.0ms	(+.f64 x (neg.f64 (*.f64 z y)))
0.0ms	(+.f64 x (neg.f64 (*.f64 z y)))

series81.0ms (0.2%)

Counts

1 → 18

Calls

1 calls:

81.0ms

(+.f64 x (neg.f64 (*.f64 z y)))

Compiler

Compiled 119 to 132 computations (-10.9% saved)

simplify89.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4908	253
1	4908	253

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

2.5b	(exp.f64 (log.f64 (*.f64 z (sin.f64 y))))
0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (exp.f64 (log.f64 (*.f64 z (sin.f64 y)))))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 z (sin.f64 y))
2.5b	(exp.f64 (log.f64 (*.f64 z (sin.f64 y))))
6.6b	(log.f64 (*.f64 z (sin.f64 y)))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64_8323`
13×	`add-sqr-sqrt_binary64_8284`
11×	`add-exp-log_binary64_8300`
9×	`add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
8×	`add-cbrt-cube_binary64_8298`
6×	`associate-l_binary64_8203` `associate-r_binary64_8202`
5×	`exp-prod_binary64_8314`
4×	`log-pow_binary64_8351` `pow-prod-down_binary64_8333` `add-log-exp_binary64_8301`
3×	`prod-exp_binary64_8311`
2×	`rem-log-exp_binary64_8303` `unswap-sqr_binary64_8230` `cbrt-unprod_binary64_8295` `*-commutative_binary64_8193` `log-prod_binary64_8348`
1×	`exp-sum_binary64_8308` `rem-exp-log_binary64_8302`

Counts

4 → 62

Calls

8 calls:

4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(*.f64 x (cos.f64 y))
4.0ms	(exp.f64 (log.f64 (*.f64 z (sin.f64 y))))
3.0ms	(log.f64 (*.f64 z (sin.f64 y)))
0.0ms	(-.f64 (.f64 1 (.f64 x (cos.f64 y))) (exp.f64 (log.f64 (*.f64 z (sin.f64 y)))))

series490.0ms (1.5%)

Counts

4 → 28

Calls

4 calls:

186.0ms	(exp.f64 (log.f64 (*.f64 z (sin.f64 y))))
167.0ms	(log.f64 (*.f64 z (sin.f64 y)))
72.0ms	(*.f64 x (cos.f64 y))
64.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 805 to 720 computations (10.6% saved)

simplify130.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4900	731
1	4900	731

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (sin.f64 y) (sqrt.f64 z))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(pow.f64 (.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z))) 3)
0.0b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 z) (*.f64 (sin.f64 y) (sqrt.f64 z))) 3)))
0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 (sin.f64 y) (sqrt.f64 z))
0.2b	(.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z)))
14.9b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z))) 3))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_8284`
13×	`pow1_binary64_8323` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298`
12×	`associate-l_binary64_8203` `add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
10×	`associate-r_binary64_8202`
8×	`cbrt-prod_binary64_8293`
7×	`sqrt-prod_binary64_8278`
5×	`prod-exp_binary64_8311` `cbrt-unprod_binary64_8295` `pow-prod-down_binary64_8333`
4×	`add-log-exp_binary64_8301`
3×	`unswap-sqr_binary64_8230` `*-commutative_binary64_8193`
1×	`cube-mult_binary64_8292` `unpow3_binary64_8328` `rem-cbrt-cube_binary64_8286` `cube-prod_binary64_8290` `unpow-prod-down_binary64_8341` `sqr-pow_binary64_8234` `pow1/3_binary64_8344`

Counts

4 → 78

Calls

8 calls:

8.0ms	(.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z)))
6.0ms	(*.f64 (sin.f64 y) (sqrt.f64 z))
4.0ms	(*.f64 x (cos.f64 y))
3.0ms	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z))) 3))
0.0ms	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 z) (*.f64 (sin.f64 y) (sqrt.f64 z))) 3)))

series262.0ms (0.8%)

Counts

4 → 28

Calls

4 calls:

73.0ms	(*.f64 x (cos.f64 y))
68.0ms	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z))) 3))
62.0ms	(*.f64 (sin.f64 y) (sqrt.f64 z))
59.0ms	(.f64 (sqrt.f64 z) (.f64 (sin.f64 y) (sqrt.f64 z)))

Compiler

Compiled 827 to 693 computations (16.2% saved)

simplify74.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5114	1015

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (sin.f64 y) (cbrt.f64 z)))))
0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (sin.f64 y) (cbrt.f64 z))))))
0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)
6.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (sin.f64 y) (cbrt.f64 z))))
6.5b	(sqrt.f64 (*.f64 z (sin.f64 y)))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64_8323`
9×	`pow-prod-down_binary64_8333`
7×	`sqrt-pow1_binary64_8280`
6×	`cbrt-prod_binary64_8293` `add-sqr-sqrt_binary64_8284` `add-cube-cbrt_binary64_8297` `*-un-lft-identity_binary64_8262`
4×	`add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `add-log-exp_binary64_8301`
2×	`sqrt-prod_binary64_8278` `pow1/2_binary64_8342` `pow1/3_binary64_8344`

Counts

4 → 47

Calls

8 calls:

9.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (sin.f64 y) (cbrt.f64 z))))
3.0ms	(sqrt.f64 (*.f64 z (sin.f64 y)))
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)
0.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (sin.f64 y) (cbrt.f64 z))))))

series294.0ms (0.9%)

Counts

4 → 18

Calls

4 calls:

87.0ms	(cbrt.f64 z)
80.0ms	(cbrt.f64 z)
67.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (sin.f64 y) (cbrt.f64 z))))
59.0ms	(sqrt.f64 (*.f64 z (sin.f64 y)))

Compiler

Compiled 881 to 625 computations (29.1% saved)

simplify101.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4866	456
1	4866	456

prune5.5s (16.4%)

Pruning

304 alts after pruning (288 fresh and 16 done)

	Pruned	Kept	Total
New	299	76	375
Fresh	5	212	217
Picked	0	0	0
Done	0	16	16
Total	304	304	608

Error

0.0b

Counts

608 → 304

Compiler

Compiled 4127 to 1180 computations (71.4% saved)

simplify287.0ms (0.9%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5040	16388

regimes2.8s (8.3%)

Compiler: Compiled 25800 to 18126 computations (29.7% saved)

bsearch0.0ms (0%)

regimes207.0ms (0.6%)

Compiler: Compiled 411 to 423 computations (-2.9% saved)

bsearch62.0ms (0.2%)

Steps

Iters	Range		Point
8	1.0689401734555106e+64	5.012334080328614e+66	6.883527615635147e+64
9	-4.599883269942089e+100	-7.180335134034047e+92	-1.200477246076265e+95

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes126.0ms (0.4%)

Compiler: Compiled 156 to 180 computations (-15.4% saved)

bsearch136.0ms (0.4%)

Steps

Iters	Range		Point
6	1.0084362699042605e+235	5.0121563607951537e+235	4.964768059498051e+235
7	1.4885582305243611e-12	2.7793414898404237e-10	2.710610693309144e-10
11	-30350177010.796318	-6.643223422266248e-21	-0.0007837728650564244
4	-2.2978768204984526e+42	-1.1697830987560655e+42	-2.0866100708274394e+42
9	-1.829163848829988e+97	-4.274246619920228e+87	-2.987572139209016e+94

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes99.0ms (0.3%)

Compiler: Compiled 141 to 162 computations (-14.9% saved)

bsearch45.0ms (0.1%)

Steps

Iters	Range		Point
7	1.4885582305243611e-12	2.7793414898404237e-10	2.710610693309144e-10
11	-30350177010.796318	-6.643223422266248e-21	-0.00012454247102483822

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes43.0ms (0.1%)

Compiler: Compiled 129 to 147 computations (-14% saved)

bsearch0.0ms (0%)

regimes62.0ms (0.2%)

Compiler: Compiled 30 to 78 computations (-160% saved)

bsearch69.0ms (0.2%)

Steps

Iters	Range		Point
11	2.2588775521664867e-200	9.353275491033567e-173	1.372989190797458e-177
8	-4.866433516027052e-26	-1.851213501271855e-30	-1.3864080488888556e-26

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes27.0ms (0.1%)

Accuracy

Total 0.1b remaining (92.8%)

Threshold costs 0.1b (92.8%)

Compiler

Compiled 18 to 63 computations (-250% saved)

bsearch7.0ms (0%)

Compiler: Compiled 119 to 79 computations (33.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	102	169
1	102	169

end0.0ms (0%)

sample8.1s (24%)

Algorithm

1×

intervals

Results

561.0ms	2057×	body	1024	valid
319.0ms	4458×	body	128	valid
197.0ms	991×	body	512	valid
65.0ms	489×	body	256	valid
2.0ms	5×	body	2048	valid

Compiler

Compiled 6793 to 4778 computations (29.7% saved)

Pareto

0.01807690585517872