Details

analyze418.0ms (4.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5007	54
0	2	2
1	2	2

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
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample26.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5241	29

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

13.1b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.4b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
5.7b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
6.3b	(-.f64 (.f64 b b) (.f64 a a))

rewrite674.0ms (7.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

251×	`times-frac_binary64_425`
178×	`add-sqr-sqrt_binary64_441`
153×	`*-un-lft-identity_binary64_419`
121×	`add-cube-cbrt_binary64_454`
58×	`associate-l_binary64_360`
46×	`difference-of-squares_binary64_388`
40×	`cancel-sign-sub-inv_binary64_385`
22×	`div-inv_binary64_416`
19×	`associate-r_binary64_359`
18×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
14×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `distribute-lft-out--_binary64_371`
13×	`associate-/l*_binary64_364`
8×	`add-log-exp_binary64_458`
6×	`pow1_binary64_480` `flip3--_binary64_423` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`sub-neg_binary64_412` `associate-/r/_binary64_365` `associate-/r*_binary64_363`
3×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-sub_binary64_428` `frac-times_binary64_429` `unswap-sqr_binary64_387` `associate-*r/_binary64_361`
2×	`diff-log_binary64_511`
1×	`pow-prod-down_binary64_490` `associate-l/_binary64_362` `-commutative_binary64_350` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l/_binary64_366`

Counts

4 → 270

Calls

4 calls:

55.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
17.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
16.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 8765 to 4259 computations (51.4% saved)

series550.0ms (6%)

Error

6.0b

Counts

4 → 45

Calls

4 calls:

156.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
122.0ms	(-.f64 (.f64 b b) (.f64 a a))
115.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
111.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 2139 to 1675 computations (21.7% saved)

simplify178.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5126	8519

prune490.0ms (5.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	306	9	315
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	308	9	317

Error

0.0b

Counts

317 → 9

Compiler

Compiled 8917 to 4252 computations (52.3% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
0.2b	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))

rewrite206.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

98×	`times-frac_binary64_425`
79×	`*-un-lft-identity_binary64_419`
60×	`add-exp-log_binary64_457`
51×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
39×	`add-cbrt-cube_binary64_455`
29×	`div-exp_binary64_470`
19×	`prod-exp_binary64_468`
17×	`cbrt-undiv_binary64_453`
14×	`distribute-lft-out_binary64_370` `associate-/l*_binary64_364`
10×	`cbrt-unprod_binary64_452`
7×	`div-inv_binary64_416`
6×	`1-exp_binary64_463`
5×	`associate-/r*_binary64_363`
2×	`pow1_binary64_480` `add-log-exp_binary64_458` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l/_binary64_366` `associate-/r/_binary64_365`
1×	`flip3-+_binary64_422` `flip-+_binary64_393` `associate-*l/_binary64_362`

Counts

2 → 122

Calls

2 calls:

17.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))
15.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))

Compiler

Compiled 2889 to 1439 computations (50.2% saved)

series229.0ms (2.5%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

116.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 a b)) 1) (.f64 a b))
90.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 a b))

Compiler

Compiled 1194 to 904 computations (24.3% saved)

simplify156.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4956	3080
1	4956	3080

prune176.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Error

Counts

155 → 7

Compiler

Compiled 2912 to 1421 computations (51.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1/2 (+.f64 b a))
0.2b	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
0.3b	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))

rewrite188.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

63×	`add-exp-log_binary64_457`
42×	`add-cbrt-cube_binary64_455`
35×	`*-un-lft-identity_binary64_419`
29×	`prod-exp_binary64_468`
26×	`add-sqr-sqrt_binary64_441` `times-frac_binary64_425`
21×	`add-cube-cbrt_binary64_454`
20×	`div-exp_binary64_470`
18×	`associate-r_binary64_359`
16×	`cbrt-unprod_binary64_452`
12×	`cbrt-undiv_binary64_453`
7×	`distribute-lft-out_binary64_370`
6×	`1-exp_binary64_463`
5×	`pow1_binary64_480` `associate-/r*_binary64_363`
4×	`associate-/r/_binary64_365` `associate-/l*_binary64_364`
3×	`add-log-exp_binary64_458` `associate-l_binary64_360` `div-inv_binary64_416`
2×	`unswap-sqr_binary64_387` `associate-*r/_binary64_361` `flip3-+_binary64_422` `flip-+_binary64_393` `frac-2neg_binary64_430` `clear-num_binary64_418`
1×	`pow-prod-down_binary64_490` `-commutative_binary64_350` `associate-l/_binary64_362` `associate-/l/_binary64_366`

Counts

3 → 106

Calls

3 calls:

26.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
15.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
10.0ms	(/.f64 1/2 (+.f64 b a))

Compiler

Compiled 2308 to 1153 computations (50% saved)

series343.0ms (3.7%)

Error

Counts

3 → 36

Calls

3 calls:

124.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
97.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
62.0ms	(/.f64 1/2 (+.f64 b a))

Compiler

Compiled 1824 to 1396 computations (23.5% saved)

simplify107.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4962	2232
1	4962	2232

prune148.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	143	6	149

Error

Counts

149 → 6

Compiler

Compiled 2526 to 1254 computations (50.4% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b

(/.f64 (*.f64 (*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))) 1) (*.f64 a b))

0.3b

(*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a)))

0.4b

(/.f64 (sqrt.f64 1/2) (+.f64 b a))

rewrite275.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

114×	`add-exp-log_binary64_457`
73×	`add-cbrt-cube_binary64_455`
61×	`*-un-lft-identity_binary64_419` `prod-exp_binary64_468`
49×	`times-frac_binary64_425`
35×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
34×	`cbrt-unprod_binary64_452`
33×	`div-exp_binary64_470`
30×	`associate-r_binary64_359`
27×	`sqrt-prod_binary64_435`
19×	`cbrt-undiv_binary64_453`
13×	`distribute-lft-out_binary64_370`
10×	`1-exp_binary64_463`
8×	`pow1_binary64_480`
7×	`associate-/l*_binary64_364`
5×	`associate-/r*_binary64_363`
4×	`associate-/r/_binary64_365`
3×	`add-log-exp_binary64_458` `div-inv_binary64_416` `pow-prod-down_binary64_490`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `flip-+_binary64_393` `associate-*r/_binary64_361`
1×	`associate-l_binary64_360` `-commutative_binary64_350` `associate-l/_binary64_362` `associate-/l/_binary64_366`

Counts

3 → 146

Calls

3 calls:

16.0ms

(/.f64 (*.f64 (*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))) 1) (*.f64 a b))

14.0ms

(*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a)))

11.0ms

(/.f64 (sqrt.f64 1/2) (+.f64 b a))

Compiler

Compiled 4061 to 2453 computations (39.6% saved)

series470.0ms (5.1%)

Error

Counts

3 → 36

Calls

3 calls:

175.0ms

(/.f64 (*.f64 (*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))) 1) (*.f64 a b))

165.0ms

(*.f64 (*.f64 PI.f64 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (+.f64 b a)))

79.0ms

(/.f64 (sqrt.f64 1/2) (+.f64 b a))

Compiler

Compiled 2298 to 1880 computations (18.2% saved)

simplify115.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4987	3117
1	4987	3117

prune180.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	182	6	188

Error

Counts

188 → 6

Compiler

Compiled 3532 to 1954 computations (44.7% saved)

regimes710.0ms (7.7%)

Accuracy

Total 0.2b remaining (99.9%)

Threshold costs 0.2b (99.9%)

Compiler

Compiled 8407 to 6261 computations (25.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	17
1	16	17

end0.0ms (0%)

sample3.5s (37.4%)

Algorithm

1×

intervals

Results

531.0ms	8000×	body	128	valid
22.0ms	348×	body	128	invalid

Compiler

Compiled 2820 to 2102 computations (25.5% saved)

Details

analyze418.0ms (4.5%)

sample26.0ms (0.3%)

simplify71.0ms (0.8%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite674.0ms (7.3%)

series550.0ms (6%)

simplify178.0ms (1.9%)

prune490.0ms (5.3%)

localize18.0ms (0.2%)

rewrite206.0ms (2.2%)

series229.0ms (2.5%)

simplify156.0ms (1.7%)

prune176.0ms (1.9%)

localize8.0ms (0.1%)

rewrite188.0ms (2%)

series343.0ms (3.7%)

simplify107.0ms (1.2%)

prune148.0ms (1.6%)

localize17.0ms (0.2%)

rewrite275.0ms (3%)

series470.0ms (5.1%)

simplify115.0ms (1.2%)

prune180.0ms (1.9%)

regimes710.0ms (7.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.5s (37.4%)

Profiling