Details

analyze1.7s (12.7%)

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)

sample193.0ms (1.4%)

Algorithm

1×

intervals

Results

115.0ms	131×	body	2048	valid
33.0ms	79×	body	1024	valid
7.0ms	304×	pre	128	true
7.0ms	29×	body	512	valid
6.0ms	18×	body	1024	overflowed
5.0ms	9×	body	2048	overflowed
2.0ms	8×	body	512	overflowed
2.0ms	1×	body	4096	valid
1.0ms	11×	body	128	valid
1.0ms	5×	body	256	valid
1.0ms	5×	body	256	overflowed
1.0ms	8×	body	128	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify182.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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

Merged error: 61.3b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.4b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
6.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_789`
26×	`*-un-lft-identity_binary64_767`
15×	`cancel-sign-sub-inv_binary64_733`
11×	`add-cube-cbrt_binary64_802`
10×	`add-log-exp_binary64_806` `difference-of-squares_binary64_736`
9×	`flip--_binary64_742` `flip3--_binary64_771`
7×	`associate-l_binary64_708` `associate-r_binary64_707`
6×	`add-exp-log_binary64_805` `pow1_binary64_828` `add-cbrt-cube_binary64_803`
5×	`sub-neg_binary64_760` `distribute-lft-out--_binary64_719` `difference-of-sqr-1_binary64_737`
4×	`frac-times_binary64_777` `distribute-rgt-in_binary64_717` `distribute-lft-in_binary64_716`
3×	`diff-log_binary64_859`
2×	`associate-r/_binary64_709` `associate-l/_binary64_710`
1×	`unswap-sqr_binary64_735` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `*-commutative_binary64_698` `pow-prod-down_binary64_838`

Counts

4 → 96

Calls

4 calls:

13.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
6.0ms	(-.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)

series254.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
81.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
41.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
41.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4986	2058
1	4986	2058

prune159.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Merged error: 50.1b

Counts

109 → 4

Compiler

Compiled 3941 to 1800 computations (54.3% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
8.0b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
8.1b	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
16.3b	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_805`
14×	`add-cbrt-cube_binary64_803`
12×	`add-sqr-sqrt_binary64_789`
11×	`pow1_binary64_828`
10×	`prod-exp_binary64_816` `*-un-lft-identity_binary64_767`
8×	`add-log-exp_binary64_806`
7×	`add-cube-cbrt_binary64_802`
6×	`cbrt-unprod_binary64_800`
4×	`associate-l_binary64_708` `associate-r_binary64_707` `pow-prod-down_binary64_838`
3×	`cancel-sign-sub-inv_binary64_733`
2×	`-commutative_binary64_698` `flip-+_binary64_741` `associate-r/_binary64_709` `flip3-+_binary64_770` `difference-of-squares_binary64_736`
1×	`pow-to-exp_binary64_836` `unswap-sqr_binary64_735` `pow-exp_binary64_835` `sub-neg_binary64_760` `distribute-rgt-in_binary64_717` `diff-log_binary64_859` `distribute-lft-out--_binary64_719` `+-commutative_binary64_697` `sum-log_binary64_858` `distribute-lft-in_binary64_716` `flip--_binary64_742` `flip3--_binary64_771` `difference-of-sqr-1_binary64_737`

Counts

4 → 71

Calls

4 calls:

13.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.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))))
7.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series411.0ms (3%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))
79.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
75.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
74.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4933	1533
1	4933	1533

prune168.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Merged error: 48.9b

Counts

87 → 3

Compiler

Compiled 4242 to 2109 computations (50.3% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 eps 1/6) a))))
1.4b	(/.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)))
2.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
6.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
15×	`add-sqr-sqrt_binary64_789`
13×	`*-un-lft-identity_binary64_767`
9×	`add-log-exp_binary64_806`
8×	`associate-/r/_binary64_713`
7×	`add-cube-cbrt_binary64_802`
6×	`cancel-sign-sub-inv_binary64_733` `flip--_binary64_742` `flip3--_binary64_771`
5×	`pow1_binary64_828`
4×	`frac-times_binary64_777` `cbrt-undiv_binary64_801` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `associate-*r/_binary64_709` `div-exp_binary64_818` `difference-of-squares_binary64_736`
3×	`unpow-prod-down_binary64_846` `flip-+_binary64_741` `flip3-+_binary64_770` `pow-pow_binary64_839`
2×	`associate-/l/_binary64_714` `sub-neg_binary64_760` `diff-log_binary64_859` `distribute-lft-out--_binary64_719` `unpow-prod-up_binary64_845` `associate-*l/_binary64_710` `difference-of-sqr-1_binary64_737`
1×	`frac-2neg_binary64_778` `pow-to-exp_binary64_836` `exp-prod_binary64_819` `associate-/r_binary64_711` `sqr-pow_binary64_739` `pow-exp_binary64_835` `times-frac_binary64_773` `pow-unpow_binary64_844` `distribute-rgt-in_binary64_717` `associate-/l_binary64_712` `exp-to-pow_binary64_829` `distribute-lft-in_binary64_716` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 86

Calls

4 calls:

18.0ms	(/.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)
5.0ms	(-.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))))

series3.6s (26.2%)

Counts

4 → 12

Calls

4 calls:

3.4s	(/.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)))
80.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
72.0ms	(pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 eps 1/6) a))))
40.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5114	3445

prune315.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 0.0b

Counts

101 → 4

Compiler

Compiled 7959 to 4282 computations (46.2% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_767`
7×	`distribute-lft-out_binary64_718`
6×	`times-frac_binary64_773`
4×	`div-inv_binary64_764`
3×	`add-log-exp_binary64_806` `add-sqr-sqrt_binary64_789` `add-cube-cbrt_binary64_802`
1×	`frac-add_binary64_775` `add-exp-log_binary64_805` `pow1_binary64_828` `flip-+_binary64_741` `+-commutative_binary64_697` `sum-log_binary64_858` `flip3-+_binary64_770` `add-cbrt-cube_binary64_803`

Counts

1 → 19

Calls

1 calls:

14.0ms

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

series20.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

20.0ms

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

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4970	287
1	4970	287

prune31.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	21	5	26

Merged error: 0.0b

Counts

26 → 5

Compiler

Compiled 503 to 387 computations (23.1% saved)

regimes46.0ms (0.3%)

Compiler: Compiled 375 to 297 computations (20.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample6.1s (44.4%)

Algorithm

1×

intervals

Results

3.6s	4163×	body	2048	valid
989.0ms	2316×	body	1024	valid
238.0ms	9758×	pre	128	true
204.0ms	376×	body	2048	overflowed
194.0ms	591×	body	1024	overflowed
184.0ms	726×	body	512	valid
72.0ms	314×	body	512	overflowed
42.0ms	546×	body	128	valid
38.0ms	238×	body	256	valid
25.0ms	174×	body	256	overflowed
22.0ms	300×	body	128	overflowed
16.0ms	11×	body	4096	valid
2.0ms	3×	body	2048	invalid

Compiler

Compiled 168 to 134 computations (20.2% saved)

Details

analyze1.7s (12.7%)

sample193.0ms (1.4%)

simplify182.0ms (1.3%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite41.0ms (0.3%)

series254.0ms (1.9%)

simplify71.0ms (0.5%)

prune159.0ms (1.2%)

localize30.0ms (0.2%)

rewrite42.0ms (0.3%)

series411.0ms (3%)

simplify76.0ms (0.6%)

prune168.0ms (1.2%)

localize26.0ms (0.2%)

rewrite48.0ms (0.4%)

series3.6s (26.2%)

simplify63.0ms (0.5%)

prune315.0ms (2.3%)

localize5.0ms (0%)

rewrite15.0ms (0.1%)

series20.0ms (0.1%)

simplify60.0ms (0.4%)

prune31.0ms (0.2%)

regimes46.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.1s (44.4%)

Profiling