Details

analyze43.0ms (1.5%)

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%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample14.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	7×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	188	12
1	188	12

prune2.0ms (0.1%)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.2b	(*.f64 y (sqrt.f64 x))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
6×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
4×	`pow1_binary64` `associate-+l+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
3×	`associate-l_binary64` `cancel-sign-sub-inv_binary64`
2×	`unswap-sqr_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-+l-_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

2 → 39

Calls

2 calls:

8.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
6.0ms	(*.f64 y (sqrt.f64 x))

series101.0ms (3.6%)

Counts

2 → 6

Calls

2 calls:

55.0ms	(*.f64 y (sqrt.f64 x))
45.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

simplify56.0ms (2%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5110	594

prune100.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	38	7	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	8	46

Merged error: 0.0b

Counts

46 → 8

Compiler

Compiled 1609 to 951 computations (40.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.4b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite34.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`sqrt-pow1_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`*-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

12.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
10.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series336.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(sqrt.f64 (sqrt.f64 x))
98.0ms	(sqrt.f64 (sqrt.f64 x))
76.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
59.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5315	1029

prune119.0ms (4.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	100	8	108

Merged error: 0b

Counts

108 → 8

Compiler

Compiled 2297 to 1053 computations (54.2% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
0.4b	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))

rewrite54.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`sqrt-prod_binary64`
33×	`associate-r_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`pow1_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `sqrt-pow1_binary64`
3×	`unswap-sqr_binary64` `*-commutative_binary64`
2×	`pow1/2_binary64` `rem-sqrt-square_binary64`

Counts

4 → 102

Calls

4 calls:

20.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
14.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
8.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series372.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
100.0ms	(sqrt.f64 (sqrt.f64 x))
76.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
66.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))

simplify62.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4978	1493
1	4978	1493

prune110.0ms (3.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	114	8	122

Merged error: 0b

Counts

122 → 8

Compiler

Compiled 2526 to 878 computations (65.2% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.4b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)))
0.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3))
0.7b	(pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)

rewrite50.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-prod_binary64`
48×	`cbrt-prod_binary64`
36×	`associate-r_binary64` `add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
27×	`unpow-prod-down_binary64` `cube-prod_binary64`
14×	`pow1_binary64`
12×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
5×	`pow-pow_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `prod-exp_binary64`
3×	`pow-unpow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow1/2_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 141

Calls

4 calls:

18.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)))
8.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
6.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)
5.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3))

series395.0ms (14%)

Counts

4 → 12

Calls

4 calls:

146.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)
103.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3))
85.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
61.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)))

simplify96.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4853	1712
1	4853	1712

prune159.0ms (5.6%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	3	4
Picked	0	1	1
Done	0	3	3
Total	153	8	161

Merged error: 0b

Counts

161 → 8

Compiler

Compiled 3140 to 1448 computations (53.9% saved)

regimes52.0ms (1.8%)

Compiler: Compiled 392 to 283 computations (27.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample538.0ms (19%)

Algorithm

1×

intervals

Results

241.0ms	7999×	body	128	valid
3.0ms	125×	body	128	nan
2.0ms	66×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 141 to 104 computations (26.2% saved)

Details

analyze43.0ms (1.5%)

sample14.0ms (0.5%)

simplify14.0ms (0.5%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite17.0ms (0.6%)

series101.0ms (3.6%)

simplify56.0ms (2%)

prune100.0ms (3.5%)

localize8.0ms (0.3%)

rewrite34.0ms (1.2%)

series336.0ms (11.8%)

simplify66.0ms (2.3%)

prune119.0ms (4.2%)

localize13.0ms (0.5%)

rewrite54.0ms (1.9%)

series372.0ms (13.1%)

simplify62.0ms (2.2%)

prune110.0ms (3.9%)

localize11.0ms (0.4%)

rewrite50.0ms (1.7%)

series395.0ms (14%)

simplify96.0ms (3.4%)

prune159.0ms (5.6%)

regimes52.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample538.0ms (19%)

Profiling