Details

analyze1.8s (18.7%)

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
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 34 to 30 computations (11.8% saved)

sample68.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
18.0ms	189×	body	128	nan

Compiler

Compiled 67 to 66 computations (1.5% saved)

simplify211.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4980	44
1	4980	44

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 3.2b

Counts

2 → 1

Compiler

Compiled 58 to 50 computations (13.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.3b	(/.f64 2/3 t)
1.6b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
5.0b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_11219`
20×	`frac-sub_binary64_11207`
19×	`*-un-lft-identity_binary64_11198`
17×	`add-cube-cbrt_binary64_11230`
13×	`add-exp-log_binary64_11233` `add-cbrt-cube_binary64_11231`
12×	`times-frac_binary64_11204`
9×	`flip--_binary64_11173` `flip3--_binary64_11202`
8×	`frac-times_binary64_11208` `associate-*r/_binary64_11142`
7×	`associate-r_binary64_11140`
6×	`add-log-exp_binary64_11234` `associate-/r*_binary64_11144` `pow1_binary64_11256`
5×	`flip3-+_binary64_11201` `sqrt-prod_binary64_11213` `flip-+_binary64_11172`
4×	`associate-/l*_binary64_11145` `associate--r+_binary64_11136` `sqrt-div_binary64_11214`
3×	`sub-neg_binary64_11191` `associate-l_binary64_11141` `div-exp_binary64_11246` `cbrt-undiv_binary64_11229`
2×	`associate--l+_binary64_11137` `prod-exp_binary64_11244` `distribute-rgt-in_binary64_11150` `associate-/l/_binary64_11147` `associate-*l/_binary64_11143` `div-inv_binary64_11195` `frac-2neg_binary64_11209` `clear-num_binary64_11197` `distribute-lft-in_binary64_11149` `unswap-sqr_binary64_11166` `cbrt-unprod_binary64_11228`
1×	`pow-prod-down_binary64_11266` `distribute-lft-out_binary64_11151` `diff-log_binary64_11287` `*-commutative_binary64_11131`

Counts

4 → 104

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
12.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
8.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
3.0ms	(/.f64 2/3 t)

series624.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

383.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
128.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
92.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
21.0ms	(/.f64 2/3 t)

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4954	2992
1	4954	2992

prune206.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	4	117

Merged error: 0.0b

Counts

117 → 4

Compiler

Compiled 4702 to 2356 computations (49.9% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
1.6b	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
3.1b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))

rewrite94.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64_11219`
60×	`frac-sub_binary64_11207`
58×	`times-frac_binary64_11204`
47×	`*-un-lft-identity_binary64_11198`
46×	`associate-r_binary64_11140`
39×	`frac-times_binary64_11208`
35×	`add-cube-cbrt_binary64_11230`
31×	`cbrt-prod_binary64_11226`
28×	`sqrt-prod_binary64_11213`
27×	`associate-*r/_binary64_11142`
25×	`add-exp-log_binary64_11233` `flip--_binary64_11173` `flip3--_binary64_11202`
21×	`associate-*l/_binary64_11143`
18×	`add-cbrt-cube_binary64_11231`
10×	`unswap-sqr_binary64_11166`
9×	`flip3-+_binary64_11201` `flip-+_binary64_11172`
8×	`prod-exp_binary64_11244` `cbrt-unprod_binary64_11228`
7×	`associate-l_binary64_11141` `div-exp_binary64_11246` `cbrt-undiv_binary64_11229`
6×	`add-log-exp_binary64_11234` `pow1_binary64_11256` `distribute-lft-out_binary64_11151`
4×	`associate--r+_binary64_11136`
3×	`sub-neg_binary64_11191`
2×	`associate--l+_binary64_11137` `distribute-rgt-in_binary64_11150` `div-inv_binary64_11195` `pow1/3_binary64_11277` `distribute-lft-in_binary64_11149`
1×	`pow-prod-down_binary64_11266` `diff-log_binary64_11287` `*-commutative_binary64_11131`

Counts

4 → 166

Calls

4 calls:

28.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
24.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)

series989.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

470.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
214.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
154.0ms	(cbrt.f64 t)
151.0ms	(cbrt.f64 t)

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5026	7322

prune395.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	178	4	182

Merged error: 0.0b

Counts

182 → 4

Compiler

Compiled 9009 to 4421 computations (50.9% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 2/3 t)
3.9b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
4.1b	(log.f64 (exp.f64 (/.f64 2/3 t)))
5.0b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cube-cbrt_binary64_11230` `add-sqr-sqrt_binary64_11219` `*-un-lft-identity_binary64_11198`
21×	`times-frac_binary64_11204`
14×	`log-pow_binary64_11284`
13×	`exp-prod_binary64_11247`
11×	`add-exp-log_binary64_11233` `add-cbrt-cube_binary64_11231`
8×	`frac-sub_binary64_11207`
7×	`flip--_binary64_11173` `flip3--_binary64_11202`
6×	`add-log-exp_binary64_11234` `associate-/r*_binary64_11144`
5×	`pow1_binary64_11256`
4×	`associate-/l_binary64_11145` `frac-times_binary64_11208` `associate--r+_binary64_11136` `associate-r/_binary64_11142`
3×	`div-inv_binary64_11195` `sub-neg_binary64_11191` `log-prod_binary64_11281` `div-exp_binary64_11246` `cbrt-undiv_binary64_11229`
2×	`associate--l+_binary64_11137` `distribute-rgt-in_binary64_11150` `associate-/l/_binary64_11147` `associate-*l/_binary64_11143` `frac-2neg_binary64_11209` `clear-num_binary64_11197` `distribute-lft-in_binary64_11149` `sqrt-div_binary64_11214`
1×	`prod-exp_binary64_11244` `flip3-+_binary64_11201` `rem-log-exp_binary64_11236` `cbrt-unprod_binary64_11228` `diff-log_binary64_11287` `flip-+_binary64_11172`

Counts

4 → 98

Calls

4 calls:

15.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
6.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
4.0ms	(/.f64 2/3 t)

series780.0ms (8%)

Counts

4 → 12

Calls

4 calls:

495.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
134.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
125.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
26.0ms	(/.f64 2/3 t)

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4968	2291
1	4968	2291

prune184.0ms (1.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Merged error: 0.0b

Counts

114 → 4

Compiler

Compiled 4313 to 2226 computations (48.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
0.0b	(+.f64 a 5/6)
0.1b	(*.f64 c (+.f64 a 5/6))
1.1b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_11219`
15×	`associate-r_binary64_11140` `*-un-lft-identity_binary64_11198`
10×	`add-exp-log_binary64_11233`
9×	`add-cube-cbrt_binary64_11230`
8×	`add-log-exp_binary64_11234` `add-cbrt-cube_binary64_11231`
6×	`unpow-prod-down_binary64_11274` `pow1_binary64_11256` `associate-l_binary64_11141`
5×	`unswap-sqr_binary64_11166`
4×	`associate--l+_binary64_11137` `prod-exp_binary64_11244`
3×	`distribute-rgt-in_binary64_11150` `distribute-lft-in_binary64_11149` `associate-*r/_binary64_11142` `unpow-prod-up_binary64_11273`
2×	`sqr-pow_binary64_11170` `distribute-lft-out_binary64_11151` `sub-neg_binary64_11191` `flip3-+_binary64_11201` `exp-lft-sqr_binary64_11250` `cbrt-unprod_binary64_11228` `flip-+_binary64_11172` `*-commutative_binary64_11131`
1×	`+-commutative_binary64_11130` `sum-log_binary64_11286` `pow-to-exp_binary64_11264` `flip--_binary64_11173` `pow-prod-down_binary64_11266` `flip3--_binary64_11202` `pow-sub_binary64_11271` `diff-log_binary64_11287` `pow-exp_binary64_11263`

Counts

4 → 79

Calls

4 calls:

8.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
8.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))
7.0ms	(*.f64 c (+.f64 a 5/6))
4.0ms	(+.f64 a 5/6)

series359.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
55.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))
54.0ms	(*.f64 c (+.f64 a 5/6))
21.0ms	(+.f64 a 5/6)

simplify86.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4951	1406
1	4951	1406

prune109.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	91	4	95

Merged error: 0.0b

Counts

95 → 4

Compiler

Compiled 2141 to 1245 computations (41.8% saved)

regimes742.0ms (7.6%)

Compiler: Compiled 10152 to 8096 computations (20.3% saved)

bsearch3.0ms (0%)

Compiler: Compiled 24 to 23 computations (4.2% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	395	121
1	395	121

end0.0ms (0%)

sample2.6s (27%)

Algorithm

1×

intervals

Results

810.0ms	8000×	body	128	valid
505.0ms	5076×	body	128	nan

Compiler

Compiled 993 to 771 computations (22.4% saved)

Details

analyze1.8s (18.7%)

sample68.0ms (0.7%)

simplify211.0ms (2.2%)

prune5.0ms (0.1%)

localize23.0ms (0.2%)

rewrite53.0ms (0.5%)

series624.0ms (6.4%)

simplify63.0ms (0.6%)

prune206.0ms (2.1%)

localize31.0ms (0.3%)

rewrite94.0ms (1%)

series989.0ms (10.1%)

simplify89.0ms (0.9%)

prune395.0ms (4%)

localize26.0ms (0.3%)

rewrite46.0ms (0.5%)

series780.0ms (8%)

simplify70.0ms (0.7%)

prune184.0ms (1.9%)

localize15.0ms (0.2%)

rewrite34.0ms (0.3%)

series359.0ms (3.7%)

simplify86.0ms (0.9%)

prune109.0ms (1.1%)

regimes742.0ms (7.6%)

bsearch3.0ms (0%)

simplify13.0ms (0.1%)

end0.0ms (0%)

sample2.6s (27%)

Profiling