Details

analyze575.0ms (5.1%)

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)

sample44.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	36×	body	2048	valid
10.0ms	169×	body	128	valid
6.0ms	26×	body	1024	valid
4.0ms	11×	body	4096	valid
3.0ms	10×	body	128	invalid
1.0ms	10×	body	512	valid
1.0ms	15×	body	128	nan
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify570.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (379.0ms)

Iter	Nodes	Cost
0	1706	24
1	1706	24

prune6.0ms (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: 34.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.1%)

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))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1123`
14×	`*-un-lft-identity_binary64_1101`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
6×	`difference-of-squares_binary64_1070` `sqrt-prod_binary64_1117` `associate-/l*_binary64_1046` `times-frac_binary64_1107`
5×	`pow1_binary64_1162`
4×	`flip--_binary64_1076` `flip3--_binary64_1105` `cancel-sign-sub-inv_binary64_1067`
3×	`distribute-lft-out--_binary64_1053`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/r*_binary64_1045` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

4 → 74

Calls

4 calls:

18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
16.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series685.0ms (6%)

Counts

4 → 12

Calls

4 calls:

270.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
168.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
152.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
94.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify123.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4908	1983
1	4908	1983

prune174.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	76	10	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	10	87

Merged error: 7.7b

Counts

87 → 10

Compiler

Compiled 2156 to 1302 computations (39.6% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.5b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
12.9b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite80.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
22×	`times-frac_binary64_1107`
21×	`*-un-lft-identity_binary64_1101`
17×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
13×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
12×	`add-sqr-sqrt_binary64_1123`
11×	`add-cube-cbrt_binary64_1136` `associate-/l*_binary64_1046`
6×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
5×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162` `associate-/r*_binary64_1045`
4×	`flip3-+_binary64_1104` `div-inv_binary64_1098` `flip-+_binary64_1075`
3×	`sqrt-prod_binary64_1117`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-div_binary64_1118`
1×	`rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `+-commutative_binary64_1031` `pow1/2_binary64_1181`

Counts

4 → 102

Calls

4 calls:

25.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
24.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
9.0ms	(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))))

series1.2s (10.2%)

Counts

4 → 12

Calls

4 calls:

537.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
347.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
140.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
136.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5447	3147

prune186.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Merged error: 7.6b

Counts

124 → 12

Compiler

Compiled 3341 to 2060 computations (38.3% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1101`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140`
7×	`add-cube-cbrt_binary64_1136`
5×	`pow1_binary64_1162`
4×	`times-frac_binary64_1107` `associate-/r*_binary64_1045`
3×	`distribute-lft-out_binary64_1052` `sqrt-prod_binary64_1117`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `+-commutative_binary64_1031` `cancel-sign-sub-inv_binary64_1067` `pow1/2_binary64_1181`

Counts

4 → 64

Calls

4 calls:

14.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
13.0ms	(+.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)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series905.0ms (8%)

Counts

4 → 12

Calls

4 calls:

496.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
197.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
85.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify133.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4878	1672
1	4878	1672

prune186.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	76	12	88

Merged error: 7.6b

Counts

88 → 12

Compiler

Compiled 2192 to 1464 computations (33.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.5b	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 a -3))
12.9b	(/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite54.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
22×	`times-frac_binary64_1107`
21×	`*-un-lft-identity_binary64_1101`
17×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
13×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
12×	`add-sqr-sqrt_binary64_1123`
11×	`add-cube-cbrt_binary64_1136` `associate-/l*_binary64_1046`
6×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
5×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162` `associate-/r*_binary64_1045`
4×	`flip3-+_binary64_1104` `div-inv_binary64_1098` `flip-+_binary64_1075`
3×	`sqrt-prod_binary64_1117`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-div_binary64_1118`
1×	`rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `+-commutative_binary64_1031` `pow1/2_binary64_1181`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 a -3))
13.0ms	(/.f64 (.f64 (.f64 3 a) c) (+.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))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series1.2s (10.5%)

Counts

4 → 12

Calls

4 calls:

493.0ms	(/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
358.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 a -3))
192.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
156.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4925	3202
1	4925	3202

prune165.0ms (1.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	114	12	126

Merged error: 7.6b

Counts

126 → 12

Compiler

Compiled 3183 to 1949 computations (38.8% saved)

regimes1.7s (14.8%)

Compiler: Compiled 6144 to 4860 computations (20.9% saved)

bsearch123.0ms (1.1%)

Steps

Iters	Range	Point
9	3.2655091505015865e+113	1.523623840188747e+119	1.4494405112157072e+119
8	-1.971789599180125e-288	-1.3671639600104828e-291	-3.2016173609121512e-291
5	-1.2636081720066416e+78	-6.28772292992689e+77	-1.2490394173203949e+78

Iters

Range

Point

3.2655091505015865e+113

1.523623840188747e+119

1.4494405112157072e+119

-1.971789599180125e-288

-1.3671639600104828e-291

-3.2016173609121512e-291

-1.2636081720066416e+78

-6.28772292992689e+77

-1.2490394173203949e+78

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	125	92
1	125	92

end0.0ms (0%)

sample2.9s (25.8%)

Algorithm

1×

intervals

Results

404.0ms	1179×	body	2048	valid
374.0ms	5170×	body	128	valid
202.0ms	761×	body	1024	valid
174.0ms	380×	body	4096	valid
69.0ms	338×	body	512	valid
46.0ms	670×	body	128	nan
27.0ms	384×	body	128	invalid
23.0ms	172×	body	256	valid

Compiler

Compiled 1179 to 923 computations (21.7% saved)

Details

analyze575.0ms (5.1%)

sample44.0ms (0.4%)

simplify570.0ms (5%)

prune6.0ms (0.1%)

localize12.0ms (0.1%)

rewrite59.0ms (0.5%)

series685.0ms (6%)

simplify123.0ms (1.1%)

prune174.0ms (1.5%)

localize27.0ms (0.2%)

rewrite80.0ms (0.7%)

series1.2s (10.2%)

simplify79.0ms (0.7%)

prune186.0ms (1.6%)

localize29.0ms (0.3%)

rewrite48.0ms (0.4%)

series905.0ms (8%)

simplify133.0ms (1.2%)

prune186.0ms (1.6%)

localize25.0ms (0.2%)

rewrite54.0ms (0.5%)

series1.2s (10.5%)

simplify102.0ms (0.9%)

prune165.0ms (1.5%)

regimes1.7s (14.8%)

bsearch123.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.9s (25.8%)

Profiling