Details

sample201.0ms

Algorithm

intervals

Results

93.0ms	76×	body	2560	valid
65.0ms	113×	body	1280	valid
9.0ms	25×	body	640	valid
7.0ms	311×	pre	80	true
4.0ms	55×	body	80	overflowed
3.0ms	15×	body	320	valid
2.0ms	22×	body	80	valid
1.0ms	5×	body	160	valid

simplify96.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	13
5	5001	13

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 58.5b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.9b	(- (exp (* a eps)) 1.0)
3.4b	(- (exp (* b eps)) 1.0)
5.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

13.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series170.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
40.0ms	(- (exp (* a eps)) 1.0)
33.0ms	(- (exp (* b eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673

prune296.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 45.7b

Counts

89 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

3.5b	(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
5.0b	(- (exp (* (+ a b) eps)) 1.0)
14.6b	(* (pow eps 2) (pow b 2))
16.6b	(* (pow eps 3) (pow b 3))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-exp`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
11×	`add-log-exp`
10×	`unpow2`
8×	`add-cbrt-cube`
4×	`pow1`
3×	`sum-log`
2×	`cube-mult` `unpow3` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 137

Calls

4 calls:

17.0ms	(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

series458.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
39.0ms	(* (pow eps 2) (pow b 2))
64.0ms	(* (pow eps 3) (pow b 3))

simplify106.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	510	927
1	2493	815
2	5002	772

prune514.0ms

Filtered

149 candidates to 78 candidates (52.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	143	6	149
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	144	9	153

Merged error: 45.4b

Counts

153 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (exp (* a eps)) 1.0)
3.1b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
5.0b	(- (exp (* (+ a b) eps)) 1.0)
14.6b	(* (pow eps 2) (pow b 2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
12×	`*-un-lft-identity`
10×	`unpow2` `sqr-pow`
8×	`add-cube-cbrt` `associate-r` `associate-l` `associate-/r/` `add-log-exp`
6×	`pow-to-exp` `flip3--` `pow-exp` `flip--`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `diff-log` `associate-*l/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 110

Calls

4 calls:

4.0ms	(- (exp (* a eps)) 1.0)
18.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow eps 2) (pow b 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (exp (* a eps)) 1.0)
884.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow eps 2) (pow b 2))

simplify112.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	738	1419
1	4138	1141
2	5001	1141

prune390.0ms

Filtered

122 candidates to 76 candidates (62.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	127	4	131

Merged error: 0.0b

Counts

131 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

12.0ms

(+ (/ 1 b) (/ 1 a))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

(+ (/ 1 b) (/ 1 a))

simplify70.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2775	90
4	5001	90

prune30.0ms

Filtered

22 candidates to 14 candidates (63.6%)

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

regimes90.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.9s	2564×	body	2560	valid
2.0s	3402×	body	1280	valid
393.0ms	1078×	body	640	valid
219.0ms	9979×	pre	80	true
143.0ms	1977×	body	80	overflowed
85.0ms	344×	body	320	valid
35.0ms	477×	body	80	valid
22.0ms	137×	body	160	valid

Details

sample201.0ms

simplify96.0ms

prune4.0ms

localize17.0ms

rewrite27.0ms

series170.0ms

simplify43.0ms

prune296.0ms

localize29.0ms

rewrite43.0ms

series458.0ms

simplify106.0ms

prune514.0ms

localize26.0ms

rewrite38.0ms

series1.0s

simplify112.0ms

prune390.0ms

localize5.0ms

rewrite13.0ms

series11.0ms

simplify70.0ms

prune30.0ms

regimes90.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.1s

Profiling