Details

analyze454.0ms (6.5%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	45×	body	2048	valid
9.0ms	166×	body	128	valid
4.0ms	21×	body	1024	valid
2.0ms	6×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	28×	body	128	nan
1.0ms	13×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify233.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	927	24
1	927	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: 35.0b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1111`
15×	`add-sqr-sqrt_binary64_1133`
14×	`add-cube-cbrt_binary64_1146`
12×	`times-frac_binary64_1117`
8×	`add-log-exp_binary64_1150`
6×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
5×	`distribute-lft-out_binary64_1062` `pow1_binary64_1172`
4×	`associate-/l*_binary64_1056`
3×	`associate-/r*_binary64_1055` `sqrt-prod_binary64_1127`
2×	`sqrt-div_binary64_1128` `flip-+_binary64_1085` `flip3--_binary64_1115` `associate-/l/_binary64_1058` `flip3-+_binary64_1114` `flip--_binary64_1086`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `cancel-sign-sub-inv_binary64_1077` `frac-2neg_binary64_1122` `diff-log_binary64_1203` `+-commutative_binary64_1041` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sqrt-pow1_binary64_1129` `sum-log_binary64_1202` `sub-neg_binary64_1104` `clear-num_binary64_1110`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series475.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
136.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5101	2019

prune457.0ms (6.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Merged error: 4.8b

Counts

85 → 8

Compiler

Compiled 8892 to 5911 computations (33.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.5b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
8.4b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite61.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_1117`
59×	`add-sqr-sqrt_binary64_1133`
44×	`*-un-lft-identity_binary64_1111`
30×	`add-cube-cbrt_binary64_1146`
27×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
14×	`difference-of-squares_binary64_1080`
13×	`associate-/l*_binary64_1056` `sqrt-prod_binary64_1127`
10×	`div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `associate-/r/_binary64_1057`
9×	`associate-/r*_binary64_1055`
7×	`flip3--_binary64_1115` `distribute-lft-out--_binary64_1063` `flip--_binary64_1086`
6×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `cancel-sign-sub-inv_binary64_1077` `add-log-exp_binary64_1150`
5×	`pow1_binary64_1172`
2×	`sqrt-div_binary64_1128` `frac-2neg_binary64_1122` `clear-num_binary64_1110`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `associate-/l/_binary64_1058` `diff-log_binary64_1203` `sqrt-pow1_binary64_1129` `sub-neg_binary64_1104`

Counts

4 → 136

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
13.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series989.0ms (14.2%)

Counts

4 → 12

Calls

4 calls:

423.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
330.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
119.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5217	5032

prune374.0ms (5.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	147	9	156

Merged error: 4.8b

Counts

156 → 9

Compiler

Compiled 7772 to 4798 computations (38.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_1133`
28×	`*-un-lft-identity_binary64_1111`
18×	`times-frac_binary64_1117` `add-cube-cbrt_binary64_1146`
11×	`sqrt-prod_binary64_1127`
10×	`difference-of-squares_binary64_1080`
8×	`add-log-exp_binary64_1150`
7×	`cancel-sign-sub-inv_binary64_1077`
6×	`add-cbrt-cube_binary64_1147` `associate-/r*_binary64_1055` `add-exp-log_binary64_1149`
5×	`pow1_binary64_1172` `distribute-lft-out--_binary64_1063`
4×	`flip3--_binary64_1115` `flip--_binary64_1086`
3×	`associate-/l*_binary64_1056`
2×	`sqrt-div_binary64_1128` `diff-log_binary64_1203` `sub-neg_binary64_1104` `associate-/r/_binary64_1057`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `frac-2neg_binary64_1122` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110`

Counts

4 → 88

Calls

4 calls:

9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series683.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

359.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
127.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4898	2580
1	4898	2580

prune168.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	101	8	109

Merged error: 4.8b

Counts

109 → 8

Compiler

Compiled 3518 to 2209 computations (37.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
0.6b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.0b	(-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
22.3b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_1133`
28×	`*-un-lft-identity_binary64_1111`
18×	`times-frac_binary64_1117` `add-cube-cbrt_binary64_1146`
11×	`sqrt-prod_binary64_1127`
10×	`difference-of-squares_binary64_1080`
8×	`add-log-exp_binary64_1150`
6×	`add-cbrt-cube_binary64_1147` `cancel-sign-sub-inv_binary64_1077` `associate-/r*_binary64_1055` `add-exp-log_binary64_1149`
5×	`pow1_binary64_1172` `distribute-lft-out--_binary64_1063`
3×	`associate-/l*_binary64_1056`
2×	`sqrt-div_binary64_1128` `flip-+_binary64_1085` `flip3--_binary64_1115` `flip3-+_binary64_1114` `flip--_binary64_1086` `associate-/r/_binary64_1057`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `frac-2neg_binary64_1122` `diff-log_binary64_1203` `+-commutative_binary64_1041` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sqrt-pow1_binary64_1129` `sum-log_binary64_1202` `sub-neg_binary64_1104` `clear-num_binary64_1110`

Counts

4 → 87

Calls

4 calls:

10.0ms	(-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
10.0ms	(/.f64 c (-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series672.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

374.0ms	(/.f64 c (-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
126.0ms	(-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
105.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
66.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4909	2566
1	4909	2566

prune135.0ms (1.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	98	9	107

Merged error: 4.8b

Counts

107 → 9

Compiler

Compiled 3025 to 1947 computations (35.6% saved)

regimes190.0ms (2.7%)

Compiler: Compiled 609 to 489 computations (19.7% saved)

bsearch79.0ms (1.1%)

Steps

Iters	Range	Point
8	4.957873816217504e+26	6.543956784887513e+29	6.414833710235507e+29
10	4.640687976752479e-178	1.0390464259463864e-159	4.860998560804722e-178
2	-2.037639392999908e+140	-1.7814976742352606e+140	-1.9002502210936553e+140

Iters

Range

Point

4.957873816217504e+26

6.543956784887513e+29

6.414833710235507e+29

4.640687976752479e-178

1.0390464259463864e-159

4.860998560804722e-178

-2.037639392999908e+140

-1.7814976742352606e+140

-1.9002502210936553e+140

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	117	98
1	117	98

end0.0ms (0%)

sample1.5s (21%)

Algorithm

1×

intervals

Results

283.0ms	1141×	body	2048	valid
266.0ms	5123×	body	128	valid
149.0ms	730×	body	1024	valid
132.0ms	422×	body	4096	valid
58.0ms	386×	body	512	valid
36.0ms	695×	body	128	nan
21.0ms	400×	body	128	invalid
19.0ms	198×	body	256	valid

Compiler

Compiled 327 to 248 computations (24.2% saved)

Details

analyze454.0ms (6.5%)

sample41.0ms (0.6%)

simplify233.0ms (3.3%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite34.0ms (0.5%)

series475.0ms (6.8%)

simplify74.0ms (1.1%)

prune457.0ms (6.6%)

localize12.0ms (0.2%)

rewrite61.0ms (0.9%)

series989.0ms (14.2%)

simplify89.0ms (1.3%)

prune374.0ms (5.4%)

localize13.0ms (0.2%)

rewrite37.0ms (0.5%)

series683.0ms (9.8%)

simplify80.0ms (1.1%)

prune168.0ms (2.4%)

localize14.0ms (0.2%)

rewrite40.0ms (0.6%)

series672.0ms (9.6%)

simplify87.0ms (1.3%)

prune135.0ms (1.9%)

regimes190.0ms (2.7%)

bsearch79.0ms (1.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (21%)

Profiling