Details

analyze356.0ms (4%)

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)

sample28.0ms (0.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5241	29

prune5.0ms (0.1%)

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

11.7b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.6b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.3b	(-.f64 (.f64 b b) (.f64 a a))
7.8b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite491.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

251×	`times-frac_binary64_766`
178×	`add-sqr-sqrt_binary64_782`
153×	`*-un-lft-identity_binary64_760`
121×	`add-cube-cbrt_binary64_795`
58×	`associate-l_binary64_701`
46×	`difference-of-squares_binary64_729`
40×	`cancel-sign-sub-inv_binary64_726`
22×	`div-inv_binary64_757`
19×	`associate-r_binary64_700`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `distribute-lft-out--_binary64_712`
13×	`associate-/l*_binary64_705`
8×	`add-log-exp_binary64_799`
6×	`pow1_binary64_821` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `flip3--_binary64_764` `flip--_binary64_735`
4×	`sub-neg_binary64_753` `associate-/r/_binary64_706` `associate-/r*_binary64_704`
3×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `frac-sub_binary64_769` `frac-times_binary64_770` `unswap-sqr_binary64_728` `associate-*r/_binary64_702`
2×	`diff-log_binary64_852`
1×	`pow-prod-down_binary64_831` `associate-l/_binary64_703` `-commutative_binary64_691` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

4 → 270

Calls

4 calls:

49.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
15.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.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)

series515.0ms (5.8%)

Error

7.9b

Counts

4 → 60

Calls

4 calls:

152.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
139.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
96.0ms	(-.f64 (.f64 b b) (.f64 a a))
66.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 3066 to 2385 computations (22.2% saved)

simplify138.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

330 → 330

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4981	9092
1	4981	9092

prune454.0ms (5.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	321	9	330
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	323	9	332

Error

0.0b

Counts

332 → 9

Compiler

Compiled 9336 to 4443 computations (52.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite342.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

87×	`*-un-lft-identity_binary64_760`
86×	`add-sqr-sqrt_binary64_782`
73×	`times-frac_binary64_766`
43×	`add-cube-cbrt_binary64_795`
37×	`associate-l_binary64_701`
34×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
22×	`associate-r_binary64_700`
16×	`frac-times_binary64_770` `difference-of-squares_binary64_729`
14×	`distribute-lft-out--_binary64_712`
12×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
11×	`pow1_binary64_821`
10×	`associate-l/_binary64_703` `associate-r/_binary64_702`
9×	`associate-/r*_binary64_704`
8×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `flip3--_binary64_764` `flip--_binary64_735` `div-inv_binary64_757` `associate-/r/_binary64_706`
7×	`distribute-lft-out_binary64_711`
6×	`frac-sub_binary64_769` `associate-/l*_binary64_705`
4×	`pow-prod-down_binary64_831` `add-log-exp_binary64_799`
2×	`unswap-sqr_binary64_728` `*-commutative_binary64_691` `frac-2neg_binary64_771` `clear-num_binary64_759` `flip3-+_binary64_763` `flip-+_binary64_734`

Counts

4 → 188

Calls

4 calls:

32.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
30.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
5.0ms	(/.f64 1/2 (-.f64 b a))
5.0ms	(/.f64 PI.f64 (+.f64 b a))

Compiler

Compiled 5512 to 2805 computations (49.1% saved)

series515.0ms (5.8%)

Error

0.0b

Counts

4 → 69

Calls

4 calls:

144.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
110.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
92.0ms	(/.f64 PI.f64 (+.f64 b a))
92.0ms	(/.f64 1/2 (-.f64 b a))

Compiler

Compiled 3927 to 2829 computations (28% saved)

simplify103.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4951	5489
1	4951	5489

prune290.0ms (3.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	252	5	257
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	259	7	266

Error

Counts

266 → 7

Compiler

Compiled 6565 to 3197 computations (51.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (.f64 a b)))
0.3b	(/.f64 PI.f64 (+.f64 b a))
0.5b	(/.f64 1/2 (*.f64 a b))

rewrite117.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

38×	`*-un-lft-identity_binary64_760`
31×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `times-frac_binary64_766`
29×	`add-sqr-sqrt_binary64_782`
24×	`add-cube-cbrt_binary64_795`
18×	`associate-l_binary64_701`
10×	`div-exp_binary64_811` `cbrt-undiv_binary64_794`
9×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
7×	`distribute-lft-out_binary64_711` `associate-r_binary64_700`
6×	`associate-/l*_binary64_705`
5×	`pow1_binary64_821` `associate-/r*_binary64_704`
4×	`div-inv_binary64_757` `associate-/r/_binary64_706`
3×	`add-log-exp_binary64_799`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759` `flip3-+_binary64_763` `flip-+_binary64_734` `unswap-sqr_binary64_728`
1×	`pow-prod-down_binary64_831` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `*-commutative_binary64_691`

Counts

3 → 105

Calls

3 calls:

14.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (.f64 a b)))
5.0ms	(/.f64 PI.f64 (+.f64 b a))
4.0ms	(/.f64 1/2 (*.f64 a b))

Compiler

Compiled 1996 to 697 computations (65.1% saved)

series313.0ms (3.5%)

Error

Counts

3 → 48

Calls

3 calls:

126.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (.f64 a b)))
87.0ms	(/.f64 PI.f64 (+.f64 b a))
58.0ms	(/.f64 1/2 (*.f64 a b))

Compiler

Compiled 2154 to 1511 computations (29.9% saved)

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4966	2711
1	4966	2711

prune123.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	154	6	160

Error

Counts

160 → 6

Compiler

Compiled 2688 to 1037 computations (61.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite419.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

248×	`*-un-lft-identity_binary64_760`
190×	`times-frac_binary64_766`
126×	`add-sqr-sqrt_binary64_782`
79×	`distribute-lft-out_binary64_711`
76×	`add-cube-cbrt_binary64_795`
60×	`distribute-rgt-neg-in_binary64_718`
51×	`associate-r_binary64_700`
28×	`div-inv_binary64_757`
20×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
19×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712`
18×	`associate-l_binary64_701`
12×	`associate-/l*_binary64_705`
9×	`associate-/r*_binary64_704`
8×	`add-log-exp_binary64_799` `associate-/r/_binary64_706`
6×	`pow1_binary64_821` `div-exp_binary64_811` `cbrt-undiv_binary64_794`
4×	`flip3-+_binary64_763` `flip-+_binary64_734` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728`
3×	`associate-/l/_binary64_707`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759` `flip3--_binary64_764` `flip--_binary64_735` `unsub-neg_binary64_754` `div-sub_binary64_765` `neg-sub0_binary64_755` `associate-+r-_binary64_694` `distribute-neg-frac_binary64_724` `frac-add_binary64_768` `sum-log_binary64_851`
1×	`pow-prod-down_binary64_831` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `*-commutative_binary64_691` `neg-log_binary64_853` `+-commutative_binary64_690`

Counts

4 → 225

Calls

4 calls:

55.0ms	(*.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 (+.f64 (/.f64 1/2 a) (neg.f64 (/.f64 1/2 b))) (-.f64 b a)))
28.0ms	(/.f64 (+.f64 (/.f64 1/2 a) (neg.f64 (/.f64 1/2 b))) (-.f64 b a))
22.0ms	(+.f64 (/.f64 1/2 a) (neg.f64 (/.f64 1/2 b)))
5.0ms	(/.f64 PI.f64 (+.f64 b a))

Compiler

Compiled 6478 to 3182 computations (50.9% saved)

series519.0ms (5.8%)

Error

Counts

4 → 60

Calls

4 calls:

150.0ms	(*.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 (+.f64 (/.f64 1/2 a) (neg.f64 (/.f64 1/2 b))) (-.f64 b a)))
119.0ms	(/.f64 (+.f64 (/.f64 1/2 a) (neg.f64 (/.f64 1/2 b))) (-.f64 b a))
99.0ms	(+.f64 (/.f64 1/2 a) (neg.f64 (/.f64 1/2 b)))
94.0ms	(/.f64 PI.f64 (+.f64 b a))

Compiler

Compiled 3003 to 2091 computations (30.4% saved)

simplify109.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5097	6369

prune286.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	285	6	291

Error

Counts

291 → 6

Compiler

Compiled 6971 to 3164 computations (54.6% saved)

regimes670.0ms (7.5%)

Accuracy

Total 0.2b remaining (99.9%)

Threshold costs 0.2b (99.9%)

Compiler

Compiled 9274 to 6894 computations (25.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	17
1	13	17

end0.0ms (0%)

sample2.9s (32.7%)

Algorithm

1×

intervals

Results

447.0ms	8000×	body	128	valid
20.0ms	383×	body	128	invalid

Compiler

Compiled 3109 to 2313 computations (25.6% saved)

Details

analyze356.0ms (4%)

sample28.0ms (0.3%)

simplify59.0ms (0.7%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

rewrite491.0ms (5.5%)

series515.0ms (5.8%)

simplify138.0ms (1.6%)

prune454.0ms (5.1%)

localize12.0ms (0.1%)

rewrite342.0ms (3.8%)

series515.0ms (5.8%)

simplify103.0ms (1.2%)

prune290.0ms (3.3%)

localize7.0ms (0.1%)

rewrite117.0ms (1.3%)

series313.0ms (3.5%)

simplify81.0ms (0.9%)

prune123.0ms (1.4%)

localize11.0ms (0.1%)

rewrite419.0ms (4.7%)

series519.0ms (5.8%)

simplify109.0ms (1.2%)

prune286.0ms (3.2%)

regimes670.0ms (7.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.9s (32.7%)

Profiling