Details

analyze1.7s (13.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample177.0ms (1.5%)

Algorithm

1×

intervals

Results

110.0ms	137×	body	2048	valid
27.0ms	70×	body	1024	valid
7.0ms	304×	pre	128	true
5.0ms	22×	body	512	valid
5.0ms	16×	body	1024	overflowed
4.0ms	8×	body	2048	overflowed
2.0ms	10×	body	512	overflowed
2.0ms	12×	body	256	valid
1.0ms	15×	body	128	valid
1.0ms	14×	body	128	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5217	37

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

60.5b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
1.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.6b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_782`
26×	`*-un-lft-identity_binary64_760`
15×	`cancel-sign-sub-inv_binary64_726`
11×	`add-cube-cbrt_binary64_795`
10×	`add-log-exp_binary64_799` `difference-of-squares_binary64_729`
9×	`flip--_binary64_735` `flip3--_binary64_764`
7×	`associate-r_binary64_700` `associate-l_binary64_701`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
5×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712` `sub-neg_binary64_753`
4×	`distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `frac-times_binary64_770`
3×	`diff-log_binary64_852`
2×	`associate-l/_binary64_703` `associate-r/_binary64_702`
1×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 96

Calls

4 calls:

14.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

series144.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
42.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
28.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
24.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4967	2058
1	4967	2058

prune129.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Error

50.8b

Counts

109 → 4

Compiler

Compiled 3418 to 1405 computations (58.9% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.6b	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
7.6b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
12.1b	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_798`
14×	`add-cbrt-cube_binary64_796`
12×	`add-sqr-sqrt_binary64_782`
11×	`pow1_binary64_821`
10×	`*-un-lft-identity_binary64_760` `prod-exp_binary64_809`
8×	`add-log-exp_binary64_799`
7×	`add-cube-cbrt_binary64_795`
6×	`cbrt-unprod_binary64_793`
4×	`associate-r_binary64_700` `associate-l_binary64_701` `pow-prod-down_binary64_831`
3×	`cancel-sign-sub-inv_binary64_726`
2×	`flip3-+_binary64_763` `difference-of-squares_binary64_729` `flip-+_binary64_734` `associate-r/_binary64_702` `-commutative_binary64_691`
1×	`diff-log_binary64_852` `unswap-sqr_binary64_728` `distribute-lft-in_binary64_709` `pow-exp_binary64_828` `distribute-rgt-in_binary64_710` `difference-of-sqr-1_binary64_730` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `+-commutative_binary64_690` `sum-log_binary64_851` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 71

Calls

4 calls:

12.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))
9.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
7.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series207.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))
42.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
42.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
37.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5421	1533

prune140.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	82	5	87

Error

50.3b

Counts

87 → 5

Compiler

Compiled 3814 to 1795 computations (52.9% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b	(pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 eps 1/6) a))))
3.2b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (log.f64 (pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 eps 1/6) a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
3.6b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
15×	`add-sqr-sqrt_binary64_782`
13×	`*-un-lft-identity_binary64_760`
9×	`add-log-exp_binary64_799`
8×	`associate-/r/_binary64_706`
7×	`add-cube-cbrt_binary64_795`
6×	`cancel-sign-sub-inv_binary64_726` `flip--_binary64_735` `flip3--_binary64_764`
5×	`pow1_binary64_821`
4×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `difference-of-squares_binary64_729` `frac-times_binary64_770` `associate-*r/_binary64_702` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `unpow-prod-down_binary64_839` `pow-pow_binary64_832`
2×	`diff-log_binary64_852` `associate-*l/_binary64_703` `unpow-prod-up_binary64_838` `associate-/l/_binary64_707` `difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712` `sub-neg_binary64_753`
1×	`frac-2neg_binary64_771` `exp-prod_binary64_812` `distribute-lft-in_binary64_709` `associate-/r_binary64_704` `pow-exp_binary64_828` `div-inv_binary64_757` `distribute-rgt-in_binary64_710` `associate-/l_binary64_705` `pow-to-exp_binary64_829` `exp-to-pow_binary64_822` `sqr-pow_binary64_732` `clear-num_binary64_759` `pow-unpow_binary64_837` `times-frac_binary64_766`

Counts

4 → 86

Calls

4 calls:

17.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (log.f64 (pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 eps 1/6) a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.0ms	(pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 eps 1/6) a))))

series2.0s (16.9%)

Counts

4 → 12

Calls

4 calls:

1.9s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (log.f64 (pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 eps 1/6) a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
44.0ms	(pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 eps 1/6) a))))
42.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
23.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4998	3445
1	4998	3445

prune187.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	101	2	103

Error

0.2b

Counts

103 → 2

Compiler

Compiled 4806 to 2141 computations (55.5% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_760`
7×	`distribute-lft-out_binary64_711`
6×	`times-frac_binary64_766`
4×	`div-inv_binary64_757`
3×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799` `add-sqr-sqrt_binary64_782`
1×	`flip3-+_binary64_763` `add-exp-log_binary64_798` `frac-add_binary64_768` `flip-+_binary64_734` `add-cbrt-cube_binary64_796` `+-commutative_binary64_690` `sum-log_binary64_851` `pow1_binary64_821`

Counts

1 → 19

Calls

1 calls:

14.0ms

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

series10.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4871	287
1	4871	287

prune21.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	20	4	24

Error

0.2b

Counts

24 → 4

Compiler

Compiled 255 to 197 computations (22.7% saved)

regimes335.0ms (2.8%)

Accuracy

Total 0.3b remaining (86.3%)

Threshold costs 0.3b (86.3%)

Compiler

Compiled 5278 to 3560 computations (32.6% saved)

bsearch3.0ms (0%)

Compiler: Compiled 24 to 19 computations (20.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	133
1	52	133

end0.0ms (0%)

sample6.2s (52.2%)

Algorithm

1×

intervals

Results

3.1s	4096×	body	2048	valid
921.0ms	2365×	body	1024	valid
226.0ms	9688×	pre	128	true
185.0ms	568×	body	1024	overflowed
179.0ms	375×	body	2048	overflowed
175.0ms	728×	body	512	valid
60.0ms	292×	body	512	overflowed
39.0ms	553×	body	128	valid
39.0ms	246×	body	256	valid
23.0ms	297×	body	128	overflowed
23.0ms	154×	body	256	overflowed
17.0ms	12×	body	4096	valid
2.0ms	2×	body	2048	invalid

Compiler

Compiled 1430 to 958 computations (33% saved)

Details

analyze1.7s (13.9%)

sample177.0ms (1.5%)

simplify114.0ms (1%)

prune3.0ms (0%)

localize18.0ms (0.2%)

rewrite37.0ms (0.3%)

series144.0ms (1.2%)

simplify91.0ms (0.8%)

prune129.0ms (1.1%)

localize25.0ms (0.2%)

rewrite42.0ms (0.4%)

series207.0ms (1.7%)

simplify61.0ms (0.5%)

prune140.0ms (1.2%)

localize28.0ms (0.2%)

rewrite42.0ms (0.4%)

series2.0s (16.9%)

simplify110.0ms (0.9%)

prune187.0ms (1.6%)

localize4.0ms (0%)

rewrite16.0ms (0.1%)

series10.0ms (0.1%)

simplify80.0ms (0.7%)

prune21.0ms (0.2%)

regimes335.0ms (2.8%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.2s (52.2%)

Profiling