Details

analyze341.0ms (9.5%)

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
21.8%	78%	0.1%	6
26.5%	73.3%	0.1%	7
32%	67.9%	0.1%	8
46.4%	52.7%	0.9%	9
50.9%	47.2%	1.9%	10
54.3%	43.3%	2.4%	11
62.1%	32.5%	5.4%	12
64.3%	28.1%	7.6%	13
66.3%	24.6%	9.2%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	30×	body	128	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify215.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	718	15
1	718	15

prune5.0ms (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: 0.0b

Counts

2 → 2

Compiler

Compiled 54 to 47 computations (13% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 4) y)
0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
3.4b	(*.f64 (/.f64 x y) z)

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_423`
25×	`add-sqr-sqrt_binary64_445`
22×	`times-frac_binary64_429`
20×	`add-cube-cbrt_binary64_458`
13×	`associate-l_binary64_364`
10×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
5×	`pow1_binary64_484` `add-log-exp_binary64_462`
4×	`distribute-lft-out_binary64_374` `associate-/l*_binary64_368`
3×	`associate-l/_binary64_366` `associate-r_binary64_363` `associate-/r_binary64_367`
2×	`prod-exp_binary64_472` `associate-/l/_binary64_370` `div-inv_binary64_420` `unswap-sqr_binary64_391` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `sub-neg_binary64_416` `flip-+_binary64_397` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `flip3--_binary64_427` `*-commutative_binary64_354` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `flip--_binary64_398` `sub-div_binary64_430` `frac-sub_binary64_432`

Counts

3 → 79

Calls

3 calls:

11.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
7.0ms	(*.f64 (/.f64 x y) z)
6.0ms	(/.f64 (+.f64 x 4) y)

series153.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

76.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
43.0ms	(*.f64 (/.f64 x y) z)
34.0ms	(/.f64 (+.f64 x 4) y)

simplify66.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4982	1165
1	4982	1165

prune122.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	84	6	90

Merged error: 0b

Counts

90 → 6

Compiler

Compiled 2299 to 1295 computations (43.7% saved)

localize149.0ms (4.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
1.0b	(*.f64 z (/.f64 x (cbrt.f64 y)))
2.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))

rewrite43.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-exp-log_binary64_461`
46×	`prod-exp_binary64_472`
35×	`add-cbrt-cube_binary64_459`
30×	`add-sqr-sqrt_binary64_445`
23×	`times-frac_binary64_429` `associate-r_binary64_363`
22×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
20×	`div-exp_binary64_474` `cbrt-unprod_binary64_456`
16×	`cbrt-prod_binary64_454`
11×	`pow1_binary64_484`
10×	`associate-l_binary64_364` `cbrt-undiv_binary64_457`
6×	`rec-exp_binary64_473` `1-exp_binary64_467`
4×	`pow-prod-down_binary64_494` `associate-*r/_binary64_365` `add-log-exp_binary64_462`
3×	`unswap-sqr_binary64_391`
2×	`pow1/3_binary64_505` `*-commutative_binary64_354` `div-inv_binary64_420`
1×	`frac-times_binary64_433` `associate-*l/_binary64_366`

Counts

4 → 115

Calls

4 calls:

17.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))
11.0ms	(*.f64 z (/.f64 x (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series505.0ms (14.1%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt.f64 y)
136.0ms	(cbrt.f64 y)
111.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))
106.0ms	(*.f64 z (/.f64 x (cbrt.f64 y)))

simplify90.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5011	1249

prune125.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	127	6	133

Merged error: 0b

Counts

133 → 6

Compiler

Compiled 2845 to 1271 computations (55.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (/.f64 4 y) (*.f64 (/.f64 x y) (-.f64 1 z)))
3.3b	(*.f64 (/.f64 x y) (-.f64 1 z))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_445`
17×	`*-un-lft-identity_binary64_423`
14×	`add-cube-cbrt_binary64_458`
13×	`associate-l_binary64_364`
12×	`cancel-sign-sub-inv_binary64_389`
10×	`times-frac_binary64_429`
8×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `associate-+r+_binary64_355`
7×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
6×	`associate-r_binary64_363`
5×	`frac-add_binary64_431`
4×	`sub-neg_binary64_416` `frac-times_binary64_433` `pow1_binary64_484` `flip3--_binary64_427` `associate-*r/_binary64_365` `add-log-exp_binary64_462` `flip--_binary64_398`
2×	`prod-exp_binary64_472` `associate-*l/_binary64_366` `difference-of-squares_binary64_392` `unswap-sqr_binary64_391` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `flip-+_binary64_397` `+-commutative_binary64_353` `*-commutative_binary64_354` `distribute-lft-out--_binary64_375` `flip3-+_binary64_426` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `sum-log_binary64_514`

Counts

2 → 71

Calls

2 calls:

12.0ms	(*.f64 (/.f64 x y) (-.f64 1 z))
10.0ms	(+.f64 (/.f64 4 y) (*.f64 (/.f64 x y) (-.f64 1 z)))

series151.0ms (4.2%)

Counts

2 → 6

Calls

2 calls:

81.0ms	(*.f64 (/.f64 x y) (-.f64 1 z))
69.0ms	(+.f64 (/.f64 4 y) (*.f64 (/.f64 x y) (-.f64 1 z)))

simplify54.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5126	1213

prune71.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	77	6	83

Merged error: 0b

Counts

83 → 6

Compiler

Compiled 1471 to 819 computations (44.3% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))
10.4b	(cbrt.f64 (/.f64 x y))
10.4b	(cbrt.f64 (/.f64 x y))
10.4b	(cbrt.f64 (/.f64 x y))

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64_454`
27×	`times-frac_binary64_429`
25×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
16×	`pow1_binary64_484` `add-exp-log_binary64_461`
15×	`cbrt-div_binary64_455`
10×	`add-cbrt-cube_binary64_459`
8×	`pow-prod-down_binary64_494` `prod-exp_binary64_472` `cbrt-unprod_binary64_456`
7×	`associate-*r/_binary64_365`
5×	`frac-times_binary64_433` `associate-*l/_binary64_366`
4×	`add-log-exp_binary64_462`
3×	`pow1/3_binary64_505` `div-inv_binary64_420`
1×	`associate-l_binary64_364` `-commutative_binary64_354` `associate-r*_binary64_363`

Counts

4 → 95

Calls

4 calls:

20.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))
3.0ms	(cbrt.f64 (/.f64 x y))
3.0ms	(cbrt.f64 (/.f64 x y))
3.0ms	(cbrt.f64 (/.f64 x y))

series325.0ms (9%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt.f64 (/.f64 x y))
94.0ms	(cbrt.f64 (/.f64 x y))
92.0ms	(cbrt.f64 (/.f64 x y))
44.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))

simplify96.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4935	1313
1	4935	1313

prune96.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	107	6	113

Merged error: 0b

Counts

113 → 6

Compiler

Compiled 2694 to 886 computations (67.1% saved)

regimes71.0ms (2%)

Compiler: Compiled 400 to 320 computations (20% saved)

bsearch43.0ms (1.2%)

Steps

Iters	Range		Point
8	2.2537758238713463e-16	3.4066151752852677e-13	2.2116846177386437e-13
9	-4.069238917529776e-24	-8.735617175419175e-31	-9.87444019119289e-29

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	63
1	81	63

end0.0ms (0%)

sample715.0ms (19.9%)

Algorithm

1×

intervals

Results

311.0ms	8000×	body	128	valid
45.0ms	1189×	body	128	invalid

Compiler

Compiled 148 to 115 computations (22.3% saved)

Details

analyze341.0ms (9.5%)

sample19.0ms (0.5%)

simplify215.0ms (6%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

rewrite31.0ms (0.9%)

series153.0ms (4.3%)

simplify66.0ms (1.8%)

prune122.0ms (3.4%)

localize149.0ms (4.2%)

rewrite43.0ms (1.2%)

series505.0ms (14.1%)

simplify90.0ms (2.5%)

prune125.0ms (3.5%)

localize8.0ms (0.2%)

rewrite29.0ms (0.8%)

series151.0ms (4.2%)

simplify54.0ms (1.5%)

prune71.0ms (2%)

localize13.0ms (0.4%)

rewrite40.0ms (1.1%)

series325.0ms (9%)

simplify96.0ms (2.7%)

prune96.0ms (2.7%)

regimes71.0ms (2%)

bsearch43.0ms (1.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample715.0ms (19.9%)

Profiling