Details

analyze264.0ms (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample46.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	124×	body	256	valid
9.0ms	289×	pre	128	true
7.0ms	86×	body	128	valid
6.0ms	46×	body	512	valid
2.0ms	33×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify224.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (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: 52.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
25.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_101`
14×	`*-un-lft-identity_binary64_79`
9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-cube-cbrt_binary64_114` `add-log-exp_binary64_118`
6×	`sqrt-prod_binary64_95` `times-frac_binary64_85` `associate-/l*_binary64_24` `difference-of-squares_binary64_48`
5×	`pow1_binary64_140`
4×	`flip--_binary64_54` `flip3--_binary64_83` `cancel-sign-sub-inv_binary64_45`
3×	`distribute-lft-out--_binary64_31`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `sqrt-div_binary64_96` `diff-log_binary64_171` `associate-/l/_binary64_26` `sub-neg_binary64_72`
1×	`associate-/r*_binary64_23` `div-sub_binary64_84` `div-inv_binary64_76` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `frac-2neg_binary64_90`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series519.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
128.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5031	1979

prune103.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 0.1b

Counts

87 → 4

Compiler

Compiled 2067 to 1225 computations (40.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
22×	`times-frac_binary64_85`
20×	`*-un-lft-identity_binary64_79`
17×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
13×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
11×	`associate-/l*_binary64_24`
10×	`add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101`
8×	`add-log-exp_binary64_118`
6×	`associate-/r/_binary64_25`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_53` `div-inv_binary64_76` `flip3-+_binary64_82` `pow1_binary64_140`
2×	`clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`sum-log_binary64_170` `+-commutative_binary64_9` `flip--_binary64_54` `diff-log_binary64_171` `flip3--_binary64_83` `cancel-sign-sub-inv_binary64_45` `associate-/l/_binary64_26` `sub-neg_binary64_72`

Counts

4 → 99

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series876.0ms (15.6%)

Counts

4 → 12

Calls

4 calls:

382.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
306.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
118.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
70.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4960	3037
1	4960	3037

prune161.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Merged error: 0.0b

Counts

115 → 7

Compiler

Compiled 3257 to 2009 computations (38.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_79`
15×	`add-sqr-sqrt_binary64_101`
14×	`add-cube-cbrt_binary64_114`
12×	`times-frac_binary64_85`
8×	`add-log-exp_binary64_118`
6×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
5×	`distribute-lft-out_binary64_30` `pow1_binary64_140`
4×	`associate-/r*_binary64_23`
3×	`sqrt-prod_binary64_95` `associate-/l*_binary64_24`
2×	`flip-+_binary64_53` `flip--_binary64_54` `associate-/r/_binary64_25` `sqrt-div_binary64_96` `flip3--_binary64_83` `flip3-+_binary64_82`
1×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76` `sum-log_binary64_170` `+-commutative_binary64_9` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `diff-log_binary64_171` `clear-num_binary64_78` `pow1/2_binary64_159` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

4 → 72

Calls

4 calls:

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

series645.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
139.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
65.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5087	1969

prune111.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 0b

Counts

91 → 7

Compiler

Compiled 2343 to 1463 computations (37.6% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.3b	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
0.3b	(.f64 c (.f64 (*.f64 c a) 16))
0.5b	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

rewrite58.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
27×	`pow1_binary64_140`
16×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow-prod-down_binary64_150` `*-un-lft-identity_binary64_79`
14×	`add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101`
9×	`times-frac_binary64_85`
6×	`associate-l_binary64_20` `add-log-exp_binary64_118`
3×	`associate-/r_binary64_23` `associate-/l_binary64_24`
2×	`flip-+_binary64_53` `associate-/r/_binary64_25` `-commutative_binary64_10` `associate-/l/_binary64_26` `flip3-+_binary64_82` `associate-r*_binary64_19`
1×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-sub_binary64_84` `div-inv_binary64_76` `sum-log_binary64_170` `+-commutative_binary64_9` `flip--_binary64_54` `clear-num_binary64_78` `flip3--_binary64_83` `distribute-lft-out_binary64_30` `frac-2neg_binary64_90`

Counts

4 → 89

Calls

4 calls:

15.0ms	(+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
12.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
11.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
8.0ms	(.f64 c (.f64 (*.f64 c a) 16))

series453.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
158.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
55.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
37.0ms	(.f64 c (.f64 (*.f64 c a) 16))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4952	2825
1	4952	2825

prune164.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	101	7	108

Merged error: 0b

Counts

108 → 7

Compiler

Compiled 3979 to 2356 computations (40.8% saved)

regimes62.0ms (1.1%)

Compiler: Compiled 684 to 522 computations (23.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample1.5s (26%)

Algorithm

1×

intervals

Results

369.0ms	3870×	body	256	valid
267.0ms	8808×	pre	128	true
197.0ms	1410×	body	512	valid
144.0ms	2720×	body	128	valid
38.0ms	808×	body	128	nan

Compiler

Compiled 272 to 208 computations (23.5% saved)

Details

analyze264.0ms (4.7%)

sample46.0ms (0.8%)

simplify224.0ms (4%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite37.0ms (0.7%)

series519.0ms (9.2%)

simplify71.0ms (1.3%)

prune103.0ms (1.8%)

localize14.0ms (0.2%)

rewrite52.0ms (0.9%)

series876.0ms (15.6%)

simplify75.0ms (1.3%)

prune161.0ms (2.9%)

localize12.0ms (0.2%)

rewrite32.0ms (0.6%)

series645.0ms (11.5%)

simplify69.0ms (1.2%)

prune111.0ms (2%)

localize23.0ms (0.4%)

rewrite58.0ms (1%)

series453.0ms (8.1%)

simplify70.0ms (1.3%)

prune164.0ms (2.9%)

regimes62.0ms (1.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (26%)

Profiling