Details

analyze1.5s (4.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.7%	98%	0.3%	13
2.5%	97.2%	0.3%	14

Compiler

Compiled 22 to 20 computations (9.1% saved)

sample41.0ms (0.1%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
9.0ms	158×	body	128	invalid

Compiler

Compiled 43 to 45 computations (-4.7% saved)

simplify112.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	5177	31

prune3.0ms (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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 42 to 38 computations (9.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))
0.0b	(-.f64 x (*.f64 (-.f64 y 1) z))
0.0b	(*.f64 (-.f64 (+.f64 y t) 2) b)
0.0b	(*.f64 (-.f64 y 1) z)

rewrite49.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`associate-*l/_binary64`
19×	`flip3--_binary64` `flip--_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
15×	`add-log-exp_binary64`
13×	`associate-l_binary64`
12×	`frac-add_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-sub_binary64`
6×	`associate-r_binary64`
4×	`diff-log_binary64` `associate-+l+_binary64`
3×	`sub-neg_binary64` `cancel-sign-sub-inv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `sum-log_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate--l+_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `associate-+l-_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 89

Calls

4 calls:

15.0ms	(+.f64 (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))
10.0ms	(*.f64 (-.f64 (+.f64 y t) 2) b)
8.0ms	(*.f64 (-.f64 y 1) z)
4.0ms	(-.f64 x (*.f64 (-.f64 y 1) z))

series437.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

313.0ms	(+.f64 (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))
45.0ms	(-.f64 x (*.f64 (-.f64 y 1) z))
43.0ms	(*.f64 (-.f64 (+.f64 y t) 2) b)
36.0ms	(*.f64 (-.f64 y 1) z)

simplify76.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5217	3468

prune194.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	3	102

Merged error: 0.0b

Counts

102 → 3

Compiler

Compiled 4440 to 2789 computations (37.2% saved)

localize16.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 (+.f64 y t) 2) b)
0.0b	(+.f64 (-.f64 (-.f64 (+.f64 z x) (.f64 y z)) (.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))
0.0b	(-.f64 (+.f64 z x) (*.f64 y z))

rewrite48.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-log-exp_binary64` `associate-*l/_binary64`
18×	`flip3--_binary64` `flip--_binary64`
12×	`frac-add_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`frac-sub_binary64`
7×	`diff-log_binary64`
6×	`associate-l_binary64` `sum-log_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `associate-+l+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate--l+_binary64`
3×	`sub-neg_binary64` `associate-r_binary64` `cancel-sign-sub-inv_binary64`
2×	`distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 69

Calls

3 calls:

18.0ms	(+.f64 (-.f64 (-.f64 (+.f64 z x) (.f64 y z)) (.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))
10.0ms	(*.f64 (-.f64 (+.f64 y t) 2) b)
7.0ms	(-.f64 (+.f64 z x) (*.f64 y z))

series392.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

306.0ms	(+.f64 (-.f64 (-.f64 (+.f64 z x) (.f64 y z)) (.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))
44.0ms	(*.f64 (-.f64 (+.f64 y t) 2) b)
42.0ms	(-.f64 (+.f64 z x) (*.f64 y z))

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4938	3325
1	4938	3325

prune105.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	78	3	81

Merged error: 0.0b

Counts

81 → 3

Compiler

Compiled 3154 to 1217 computations (61.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
23×	`pow1_binary64`
19×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64` `sqrt-div_binary64`
13×	`associate-l_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
8×	`swap-sqr_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64` `unswap-sqr_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `rem-sqrt-square_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`pow-sqr_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `-commutative_binary64`
1×	`rem-square-sqrt_binary64` `difference-of-sqr-1_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `distribute-lft-out--_binary64` `sqr-abs_binary64` `pow2_binary64`

Counts

4 → 112

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 (-.f64 x (.f64 (-.f64 y 1) z))) (sqrt.f64 (-.f64 x (*.f64 (-.f64 y 1) z))))
8.0ms	(*.f64 (-.f64 y 1) z)
3.0ms	(sqrt.f64 (-.f64 x (*.f64 (-.f64 y 1) z)))
3.0ms	(sqrt.f64 (-.f64 x (*.f64 (-.f64 y 1) z)))

series335.0ms (1%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(sqrt.f64 (-.f64 x (*.f64 (-.f64 y 1) z)))
97.0ms	(.f64 (sqrt.f64 (-.f64 x (.f64 (-.f64 y 1) z))) (sqrt.f64 (-.f64 x (*.f64 (-.f64 y 1) z))))
97.0ms	(sqrt.f64 (-.f64 x (*.f64 (-.f64 y 1) z)))
37.0ms	(*.f64 (-.f64 y 1) z)

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4942	2088
1	4942	2088

prune198.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	124	3	127

Merged error: 0.0b

Counts

127 → 3

Compiler

Compiled 4474 to 2821 computations (36.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)))
0.0b	(*.f64 (-.f64 y 1) z)
0.1b	(pow.f64 (+.f64 (.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) 3)
51.0b	(cbrt.f64 (pow.f64 (+.f64 (.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) 3))

rewrite91.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`associate-*l/_binary64`
49×	`flip3--_binary64` `flip--_binary64`
36×	`frac-add_binary64`
28×	`cube-div_binary64`
24×	`frac-sub_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
14×	`cbrt-div_binary64`
13×	`add-log-exp_binary64`
12×	`add-cube-cbrt_binary64` `cbrt-prod_binary64`
7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
6×	`unpow-prod-down_binary64` `cube-prod_binary64`
4×	`associate-+r+_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `diff-log_binary64` `associate-r_binary64` `flip-+_binary64` `sum-log_binary64`
2×	`sub-neg_binary64` `sqr-pow_binary64` `cancel-sign-sub-inv_binary64` `difference-of-squares_binary64` `unpow3_binary64` `associate--l+_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `associate-+r-_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `pow-pow_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

19.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) 3))
19.0ms	(pow.f64 (+.f64 (.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) 3)
18.0ms	(+.f64 (.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)))
8.0ms	(*.f64 (-.f64 y 1) z)

series26.7s (82.3%)

Counts

4 → 12

Calls

4 calls:

26.0s	(pow.f64 (+.f64 (.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) 3)
317.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) 3))
314.0ms	(+.f64 (.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)))
32.0ms	(*.f64 (-.f64 y 1) z)

simplify125.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4938	9200
1	4938	9200

prune355.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	138	3	141

Merged error: 0.0b

Counts

141 → 3

Compiler

Compiled 7657 to 4605 computations (39.9% saved)

regimes81.0ms (0.3%)

Compiler: Compiled 468 to 468 computations (0% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	123	31
1	123	31

end0.0ms (0%)

sample1.3s (4%)

Algorithm

1×

intervals

Results

478.0ms	7996×	body	128	valid
269.0ms	4593×	body	128	invalid
0.0ms	2×	body	512	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 119 to 110 computations (7.6% saved)

Details

analyze1.5s (4.6%)

sample41.0ms (0.1%)

simplify112.0ms (0.3%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite49.0ms (0.1%)

series437.0ms (1.3%)

simplify76.0ms (0.2%)

prune194.0ms (0.6%)

localize16.0ms (0%)

rewrite48.0ms (0.1%)

series392.0ms (1.2%)

simplify92.0ms (0.3%)

prune105.0ms (0.3%)

localize20.0ms (0.1%)

rewrite40.0ms (0.1%)

series335.0ms (1%)

simplify83.0ms (0.3%)

prune198.0ms (0.6%)

localize21.0ms (0.1%)

rewrite91.0ms (0.3%)

series26.7s (82.3%)

simplify125.0ms (0.4%)

prune355.0ms (1.1%)

regimes81.0ms (0.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3s (4%)

Profiling