Details

analyze1.2s (17.4%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
6.0ms	92×	body	128	invalid

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify301.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4898	19
1	4898	19

prune8.0ms (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: 12.4b

Counts

2 → 2

Compiler

Compiled 41 to 31 computations (24.4% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 z z) (.f64 x x))
0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
11.7b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

rewrite52.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_17491`
15×	`*-un-lft-identity_binary64_17469`
13×	`add-cube-cbrt_binary64_17504` `times-frac_binary64_17475`
7×	`difference-of-squares_binary64_17438` `add-log-exp_binary64_17508`
5×	`add-exp-log_binary64_17507` `add-cbrt-cube_binary64_17505`
4×	`associate-/l*_binary64_17414` `cancel-sign-sub-inv_binary64_17435`
3×	`associate-/r*_binary64_17413` `pow1_binary64_17530` `flip3--_binary64_17473` `flip--_binary64_17444`
2×	`sub-neg_binary64_17462` `associate-/l/_binary64_17416` `div-sub_binary64_17474` `diff-log_binary64_17561`
1×	`associate--l-_binary64_17407` `frac-2neg_binary64_17480` `clear-num_binary64_17468` `div-exp_binary64_17520` `cbrt-undiv_binary64_17503` `distribute-lft-out--_binary64_17421` `div-inv_binary64_17466`

Counts

3 → 65

Calls

3 calls:

23.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
12.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

series524.0ms (7.6%)

Counts

3 → 9

Calls

3 calls:

366.0ms	(-.f64 (.f64 z z) (.f64 x x))
79.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
79.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

simplify113.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5012	1382

prune125.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Merged error: 0.0b

Counts

76 → 4

Compiler

Compiled 1514 to 432 computations (71.5% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y)) y)
0.0b	(/.f64 (-.f64 z x) y)
0.2b	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))

rewrite86.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_17491`
40×	`*-un-lft-identity_binary64_17469`
31×	`times-frac_binary64_17475`
24×	`add-cube-cbrt_binary64_17504`
19×	`associate-r_binary64_17409`
10×	`add-exp-log_binary64_17507` `add-cbrt-cube_binary64_17505`
7×	`difference-of-squares_binary64_17438` `distribute-lft-out--_binary64_17421`
5×	`associate-/l*_binary64_17414` `add-log-exp_binary64_17508` `pow1_binary64_17530`
4×	`associate-l_binary64_17410`
3×	`associate-/r*_binary64_17413` `cancel-sign-sub-inv_binary64_17435`
2×	`associate-/l/_binary64_17416` `flip3-+_binary64_17472` `flip-+_binary64_17443` `prod-exp_binary64_17518` `unswap-sqr_binary64_17437` `frac-times_binary64_17479` `div-exp_binary64_17520` `cbrt-undiv_binary64_17503` `associate-*l/_binary64_17412` `cbrt-unprod_binary64_17502` `div-inv_binary64_17466` `flip3--_binary64_17473` `flip--_binary64_17444`
1×	`sub-neg_binary64_17462` `distribute-lft-out_binary64_17420` `-commutative_binary64_17400` `div-sub_binary64_17474` `associate-r/_binary64_17411` `frac-2neg_binary64_17480` `clear-num_binary64_17468` `diff-log_binary64_17561` `pow-prod-down_binary64_17540`

Counts

3 → 95

Calls

3 calls:

28.0ms	(-.f64 (*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y)) y)
28.0ms	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))
13.0ms	(/.f64 (-.f64 z x) y)

series206.0ms (3%)

Counts

3 → 9

Calls

3 calls:

91.0ms	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))
69.0ms	(-.f64 (*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y)) y)
45.0ms	(/.f64 (-.f64 z x) y)

simplify141.0ms (2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4956	1642
1	4956	1642

prune154.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	103	5	108

Merged error: 0.0b

Counts

108 → 5

Compiler

Compiled 2087 to 606 computations (71% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
0.0b	(/.f64 y (-.f64 z x))
0.3b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

rewrite160.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

177×	`times-frac_binary64_17475`
165×	`*-un-lft-identity_binary64_17469`
128×	`add-sqr-sqrt_binary64_17491`
81×	`add-cube-cbrt_binary64_17504`
26×	`associate-/r*_binary64_17413`
22×	`distribute-lft-out_binary64_17420` `difference-of-squares_binary64_17438`
20×	`distribute-lft-out--_binary64_17421`
13×	`associate-/r/_binary64_17415`
10×	`add-exp-log_binary64_17507` `add-cbrt-cube_binary64_17505`
7×	`associate-/l*_binary64_17414` `div-inv_binary64_17466` `flip3--_binary64_17473` `flip--_binary64_17444`
5×	`add-log-exp_binary64_17508`
4×	`div-exp_binary64_17520` `cbrt-undiv_binary64_17503`
3×	`cancel-sign-sub-inv_binary64_17435` `pow1_binary64_17530`
2×	`associate-/l/_binary64_17416` `frac-2neg_binary64_17480` `clear-num_binary64_17468`
1×	`sub-neg_binary64_17462` `flip3-+_binary64_17472` `flip-+_binary64_17443` `diff-log_binary64_17561`

Counts

3 → 181

Calls

3 calls:

84.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
25.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
11.0ms	(/.f64 y (-.f64 z x))

series200.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

77.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
65.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
58.0ms	(/.f64 y (-.f64 z x))

simplify174.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4976	4391
1	4976	4391

prune268.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	189	6	195

Merged error: 0b

Counts

195 → 6

Compiler

Compiled 4312 to 1056 computations (75.5% saved)

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y))) y)
0.2b	(.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)))
0.3b	(*.f64 (-.f64 z x) (/.f64 1 y))

rewrite95.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64_17507`
22×	`add-sqr-sqrt_binary64_17491`
20×	`frac-times_binary64_17479`
18×	`*-un-lft-identity_binary64_17469`
17×	`add-cbrt-cube_binary64_17505`
14×	`associate-r_binary64_17409`
13×	`add-cube-cbrt_binary64_17504` `prod-exp_binary64_17518`
11×	`times-frac_binary64_17475`
10×	`associate-r/_binary64_17411` `associate-l/_binary64_17412` `pow1_binary64_17530`
9×	`associate-l_binary64_17410` `flip3--_binary64_17473` `flip--_binary64_17444`
7×	`flip3-+_binary64_17472` `flip-+_binary64_17443` `cbrt-unprod_binary64_17502`
5×	`add-log-exp_binary64_17508`
4×	`div-exp_binary64_17520` `un-div-inv_binary64_17467` `pow-prod-down_binary64_17540`
3×	`unswap-sqr_binary64_17437` `cancel-sign-sub-inv_binary64_17435`
2×	`*-commutative_binary64_17400` `cbrt-undiv_binary64_17503` `rec-exp_binary64_17519` `1-exp_binary64_17513`
1×	`sub-neg_binary64_17462` `distribute-lft-out_binary64_17420` `difference-of-squares_binary64_17438` `diff-log_binary64_17561` `distribute-lft-out--_binary64_17421` `div-inv_binary64_17466`

Counts

3 → 99

Calls

3 calls:

34.0ms	(-.f64 (.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y))) y)
25.0ms	(.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)))
20.0ms	(*.f64 (-.f64 z x) (/.f64 1 y))

series195.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

78.0ms	(.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)))
72.0ms	(-.f64 (.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y))) y)
45.0ms	(*.f64 (-.f64 z x) (/.f64 1 y))

simplify158.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5008	1799

prune157.0ms (2.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	108	6	114

Merged error: 0b

Counts

114 → 6

Compiler

Compiled 2183 to 737 computations (66.2% saved)

regimes468.0ms (6.8%)

Compiler: Compiled 3260 to 1796 computations (44.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	19
1	32	19

end0.0ms (0%)

sample2.0s (28.8%)

Algorithm

1×

intervals

Results

631.0ms	8000×	body	128	valid
226.0ms	2858×	body	128	invalid

Compiler

Compiled 485 to 277 computations (42.9% saved)

Details

analyze1.2s (17.4%)

sample40.0ms (0.6%)

simplify301.0ms (4.4%)

prune8.0ms (0.1%)

localize17.0ms (0.2%)

rewrite52.0ms (0.8%)

series524.0ms (7.6%)

simplify113.0ms (1.6%)

prune125.0ms (1.8%)

localize17.0ms (0.2%)

rewrite86.0ms (1.2%)

series206.0ms (3%)

simplify141.0ms (2%)

prune154.0ms (2.2%)

localize18.0ms (0.3%)

rewrite160.0ms (2.3%)

series200.0ms (2.9%)

simplify174.0ms (2.5%)

prune268.0ms (3.9%)

localize19.0ms (0.3%)

rewrite95.0ms (1.4%)

series195.0ms (2.8%)

simplify158.0ms (2.3%)

prune157.0ms (2.3%)

regimes468.0ms (6.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (28.8%)

Profiling