Details

analyze782.0ms (8.6%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample59.0ms (0.6%)

Algorithm

1×

intervals

Results

17.0ms	40×	body	2048	valid
13.0ms	173×	body	128	valid
6.0ms	14×	body	4096	valid
5.0ms	18×	body	1024	valid
1.0ms	19×	body	128	nan
1.0ms	8×	body	512	valid
1.0ms	13×	body	128	invalid
0.0ms	3×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify552.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (364.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune7.0ms (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

Error

33.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.2b	(.f64 (.f64 3 a) c)
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite70.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
14×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`pow1_binary64_821`
9×	`add-cube-cbrt_binary64_795`
6×	`sqrt-prod_binary64_776` `add-log-exp_binary64_799` `difference-of-squares_binary64_729` `associate-/l*_binary64_705` `times-frac_binary64_766`
4×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
3×	`cancel-sign-sub-inv_binary64_726` `distribute-lft-out--_binary64_712` `associate-r_binary64_700` `pow-prod-down_binary64_831` `flip--_binary64_735` `flip3--_binary64_764`
2×	`cbrt-undiv_binary64_794` `associate-/l/_binary64_707` `sqrt-div_binary64_777` `div-exp_binary64_811`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `sqrt-pow1_binary64_778` `associate-/r_binary64_704` `div-inv_binary64_757` `associate-l_binary64_701` `div-sub_binary64_765` `pow1/2_binary64_840` `clear-num_binary64_759` `sub-neg_binary64_753` `-commutative_binary64_691`

Counts

4 → 80

Calls

4 calls:

23.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
10.0ms	(.f64 (.f64 3 a) c)
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series433.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
108.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
95.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
26.0ms	(.f64 (.f64 3 a) c)

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5038	1907

prune186.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Error

6.5b

Counts

93 → 9

Compiler

Compiled 2231 to 1343 computations (39.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.2b	(.f64 (.f64 3 a) c)
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_782`
10×	`pow1_binary64_821`
9×	`*-un-lft-identity_binary64_760` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
7×	`add-cube-cbrt_binary64_795`
4×	`sqrt-prod_binary64_776` `cancel-sign-sub-inv_binary64_726`
3×	`prod-exp_binary64_809` `associate-r_binary64_700` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `flip--_binary64_735` `flip3--_binary64_764`
2×	`diff-log_binary64_852` `difference-of-squares_binary64_729` `sqrt-div_binary64_777` `sub-neg_binary64_753`
1×	`rem-sqrt-square_binary64_773` `sqrt-pow1_binary64_778` `distribute-lft-out--_binary64_712` `associate-l_binary64_701` `pow1/2_binary64_840` `*-commutative_binary64_691`

Counts

4 → 62

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series236.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
84.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
26.0ms	(.f64 (.f64 3 a) c)

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4941	1226
1	4941	1226

prune135.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Error

6.5b

Counts

83 → 10

Compiler

Compiled 1742 to 1060 computations (39.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.4b	(/.f64 1/3 a)
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_782`
17×	`*-un-lft-identity_binary64_760`
15×	`add-cube-cbrt_binary64_795`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`pow1_binary64_821`
9×	`times-frac_binary64_766`
6×	`add-log-exp_binary64_799`
4×	`sqrt-prod_binary64_776`
3×	`prod-exp_binary64_809` `cancel-sign-sub-inv_binary64_726` `associate-/r_binary64_704` `associate-/l_binary64_705` `associate-r_binary64_700` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
2×	`difference-of-squares_binary64_729` `sqrt-div_binary64_777` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `distribute-lft-out--_binary64_712` `associate-l_binary64_701` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753` `*-commutative_binary64_691`

Counts

4 → 77

Calls

4 calls:

10.0ms	(.f64 (.f64 3 a) c)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(/.f64 1/3 a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series226.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
78.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
20.0ms	(.f64 (.f64 3 a) c)
19.0ms	(/.f64 1/3 a)

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4947	1222
1	4947	1222

prune127.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	90	9	99

Error

6.5b

Counts

99 → 9

Compiler

Compiled 1998 to 1212 computations (39.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.1b	(.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (/.f64 1/3 a))
9.5b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite108.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
24×	`*-un-lft-identity_binary64_760`
22×	`add-sqr-sqrt_binary64_782`
18×	`times-frac_binary64_766`
17×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
16×	`add-cube-cbrt_binary64_795`
13×	`cbrt-undiv_binary64_794` `associate-r_binary64_700` `div-exp_binary64_811`
10×	`associate-l_binary64_701`
7×	`pow1_binary64_821`
6×	`add-log-exp_binary64_799`
4×	`distribute-lft-out_binary64_711` `associate-/r/_binary64_706` `associate-/r*_binary64_704`
3×	`flip3-+_binary64_763` `sqrt-prod_binary64_776` `div-inv_binary64_757` `flip-+_binary64_734`
2×	`unswap-sqr_binary64_728` `sqrt-div_binary64_777`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `associate-l/_binary64_703` `sqrt-pow1_binary64_778` `associate-/l_binary64_705` `frac-times_binary64_770` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `pow1/2_binary64_840` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 107

Calls

4 calls:

36.0ms	(.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (/.f64 1/3 a))
27.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series637.0ms (7%)

Counts

4 → 12

Calls

4 calls:

283.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
168.0ms	(.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (/.f64 1/3 a))
101.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
85.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5092	3382

prune204.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	118	10	128

Error

6.4b

Counts

128 → 10

Compiler

Compiled 3355 to 2026 computations (39.6% saved)

regimes1.6s (17.9%)

Accuracy

Total 1.1b remaining (16.7%)

Threshold costs 0b (0%)

Compiler

Compiled 5454 to 4194 computations (23.1% saved)

bsearch175.0ms (1.9%)

Steps

Iters	Range	Point
9	1.6162187021468506e+110	1.894050897151494e+115	3.432315266375116e+113
9	-5.337491136382482e-303	9.362734650379805e-307	-1.2677949885504426e-305
8	-5.675829841425222e+150	-1.975568661264478e+148	-1.7674460872703884e+149

Iters

Range

Point

1.6162187021468506e+110

1.894050897151494e+115

3.432315266375116e+113

-5.337491136382482e-303

9.362734650379805e-307

-1.2677949885504426e-305

-5.675829841425222e+150

-1.975568661264478e+148

-1.7674460872703884e+149

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	141	94
1	141	94

end0.0ms (0%)

sample3.0s (32.9%)

Algorithm

1×

intervals

Results

428.0ms	1121×	body	2048	valid
393.0ms	5196×	body	128	valid
218.0ms	447×	body	4096	valid
204.0ms	716×	body	1024	valid
76.0ms	366×	body	512	valid
48.0ms	670×	body	128	nan
29.0ms	381×	body	128	invalid
22.0ms	154×	body	256	valid

Compiler

Compiled 1061 to 808 computations (23.8% saved)

Details

analyze782.0ms (8.6%)

sample59.0ms (0.6%)

simplify552.0ms (6.1%)

prune7.0ms (0.1%)

localize25.0ms (0.3%)

rewrite70.0ms (0.8%)

series433.0ms (4.8%)

simplify72.0ms (0.8%)

prune186.0ms (2%)

localize14.0ms (0.2%)

rewrite34.0ms (0.4%)

series236.0ms (2.6%)

simplify95.0ms (1.1%)

prune135.0ms (1.5%)

localize11.0ms (0.1%)

rewrite34.0ms (0.4%)

series226.0ms (2.5%)

simplify103.0ms (1.1%)

prune127.0ms (1.4%)

localize19.0ms (0.2%)

rewrite108.0ms (1.2%)

series637.0ms (7%)

simplify104.0ms (1.1%)

prune204.0ms (2.3%)

regimes1.6s (17.9%)

bsearch175.0ms (1.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.0s (32.9%)

Profiling