Details

analyze452.0ms (6.1%)

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)

sample39.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	179×	body	128	valid
7.0ms	30×	body	2048	valid
6.0ms	29×	body	1024	valid
2.0ms	6×	body	4096	valid
1.0ms	8×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify455.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (291.0ms)

Iter	Nodes	Cost
0	1706	24
1	1706	24

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: 30.5b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1133`
14×	`*-un-lft-identity_binary64_1111`
9×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
8×	`add-cube-cbrt_binary64_1146` `add-log-exp_binary64_1150`
6×	`times-frac_binary64_1117` `associate-/l*_binary64_1056` `difference-of-squares_binary64_1080` `sqrt-prod_binary64_1127`
5×	`pow1_binary64_1172`
4×	`cancel-sign-sub-inv_binary64_1077` `flip3--_binary64_1115` `flip--_binary64_1086`
3×	`distribute-lft-out--_binary64_1063`
2×	`sqrt-div_binary64_1128` `associate-/l/_binary64_1058` `diff-log_binary64_1203` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sub-neg_binary64_1104`
1×	`pow1/2_binary64_1191` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `associate-/r*_binary64_1055` `frac-2neg_binary64_1122` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110` `div-sub_binary64_1116`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series534.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4908	1983
1	4908	1983

prune611.0ms (8.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	74	12	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	12	87

Merged error: 5.3b

Counts

87 → 12

Compiler

Compiled 11967 to 8651 computations (27.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
2.3b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
10.2b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
22×	`times-frac_binary64_1117`
21×	`*-un-lft-identity_binary64_1111`
17×	`div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
13×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144`
12×	`add-sqr-sqrt_binary64_1133`
11×	`add-cube-cbrt_binary64_1146` `associate-/l*_binary64_1056`
6×	`add-log-exp_binary64_1150` `associate-/r/_binary64_1057`
5×	`associate-/r*_binary64_1055` `distribute-lft-out_binary64_1062` `pow1_binary64_1172`
4×	`div-inv_binary64_1108` `flip-+_binary64_1085` `flip3-+_binary64_1114`
3×	`sqrt-prod_binary64_1127`
2×	`sqrt-div_binary64_1128` `frac-2neg_binary64_1122` `clear-num_binary64_1110`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `flip3--_binary64_1115` `associate-/l/_binary64_1058` `+-commutative_binary64_1041` `sqrt-pow1_binary64_1129` `sum-log_binary64_1202` `flip--_binary64_1086`

Counts

4 → 102

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
13.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series935.0ms (12.5%)

Counts

4 → 12

Calls

4 calls:

395.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
299.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5447	3147

prune390.0ms (5.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	113	13	126

Merged error: 5.2b

Counts

126 → 13

Compiler

Compiled 8080 to 5587 computations (30.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1111`
9×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
8×	`add-sqr-sqrt_binary64_1133` `add-log-exp_binary64_1150`
7×	`add-cube-cbrt_binary64_1146`
5×	`pow1_binary64_1172`
4×	`times-frac_binary64_1117` `associate-/r*_binary64_1055`
3×	`distribute-lft-out_binary64_1062` `sqrt-prod_binary64_1127`
2×	`sqrt-div_binary64_1128` `flip-+_binary64_1085` `flip3--_binary64_1115` `flip3-+_binary64_1114` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `flip--_binary64_1086` `associate-/r/_binary64_1057`
1×	`pow1/2_binary64_1191` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `cancel-sign-sub-inv_binary64_1077` `frac-2neg_binary64_1122` `diff-log_binary64_1203` `associate-/l*_binary64_1056` `+-commutative_binary64_1041` `sqrt-pow1_binary64_1129` `sum-log_binary64_1202` `sub-neg_binary64_1104` `clear-num_binary64_1110`

Counts

4 → 64

Calls

4 calls:

11.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series657.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

357.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
115.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4878	1672
1	4878	1672

prune183.0ms (2.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	74	15	89

Merged error: 5.2b

Counts

89 → 15

Compiler

Compiled 3809 to 2684 computations (29.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1133`
17×	`*-un-lft-identity_binary64_1111`
13×	`add-cube-cbrt_binary64_1146` `associate-r_binary64_1051`
10×	`times-frac_binary64_1117`
9×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
8×	`add-log-exp_binary64_1150`
7×	`pow1_binary64_1172`
4×	`associate-l_binary64_1052`
3×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `sqrt-prod_binary64_1127`
2×	`prod-exp_binary64_1160` `associate-*l/_binary64_1054` `sqrt-div_binary64_1128` `cbrt-unprod_binary64_1144` `frac-times_binary64_1121` `flip3--_binary64_1115` `unswap-sqr_binary64_1079` `distribute-lft-out_binary64_1062` `flip--_binary64_1086`
1×	`pow1/2_binary64_1191` `-commutative_binary64_1042` `rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `cancel-sign-sub-inv_binary64_1077` `diff-log_binary64_1203` `+-commutative_binary64_1041` `div-exp_binary64_1162` `pow-prod-down_binary64_1182` `cbrt-undiv_binary64_1145` `sqrt-pow1_binary64_1129` `sum-log_binary64_1202` `sub-neg_binary64_1104` `associate-r/_binary64_1053`

Counts

4 → 76

Calls

4 calls:

14.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series478.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c))
123.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
74.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify89.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4939	2042
1	4939	2042

prune236.0ms (3.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	88	15	103

Merged error: 5.2b

Counts

103 → 15

Compiler

Compiled 4838 to 3408 computations (29.6% saved)

regimes316.0ms (4.2%)

Compiler: Compiled 1675 to 1313 computations (21.6% saved)

bsearch99.0ms (1.3%)

Steps

Iters	Range	Point
7	1.3831530327156415e+87	1.50810462671978e+89	1.474316731636549e+89
8	-3.7448139070813874e-255	-1.8350954815756547e-259	-3.4742121233166865e-259
10	-1.5872384102599588e+153	-4.592229352985525e+142	-8.575640252968764e+151

Iters

Range

Point

1.3831530327156415e+87

1.50810462671978e+89

1.474316731636549e+89

-3.7448139070813874e-255

-1.8350954815756547e-259

-3.4742121233166865e-259

-1.5872384102599588e+153

-4.592229352985525e+142

-8.575640252968764e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	149	103
1	149	103

end0.0ms (0%)

sample1.5s (20.5%)

Algorithm

1×

intervals

Results

289.0ms	1165×	body	2048	valid
272.0ms	5167×	body	128	valid
141.0ms	715×	body	1024	valid
131.0ms	409×	body	4096	valid
54.0ms	380×	body	512	valid
33.0ms	678×	body	128	nan
20.0ms	398×	body	128	invalid
16.0ms	164×	body	256	valid

Compiler

Compiled 438 to 337 computations (23.1% saved)

Details

analyze452.0ms (6.1%)

sample39.0ms (0.5%)

simplify455.0ms (6.1%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

rewrite37.0ms (0.5%)

series534.0ms (7.2%)

simplify85.0ms (1.1%)

prune611.0ms (8.2%)

localize13.0ms (0.2%)

rewrite56.0ms (0.8%)

series935.0ms (12.5%)

simplify57.0ms (0.8%)

prune390.0ms (5.2%)

localize14.0ms (0.2%)

rewrite33.0ms (0.4%)

series657.0ms (8.8%)

simplify87.0ms (1.2%)

prune183.0ms (2.5%)

localize12.0ms (0.2%)

rewrite38.0ms (0.5%)

series478.0ms (6.4%)

simplify89.0ms (1.2%)

prune236.0ms (3.2%)

regimes316.0ms (4.2%)

bsearch99.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (20.5%)

Profiling