Details

sample209.0ms

Algorithm

intervals

Results

94.0ms	89×	body	2560	valid
65.0ms	116×	body	1280	valid
10.0ms	32×	body	640	valid
8.0ms	68×	body	80	overflowed
6.0ms	325×	pre	80	true
2.0ms	8×	body	320	valid
1.0ms	12×	body	80	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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 (100.0%)

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: 61.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* b eps)) 1.0)
2.3b	(- (exp (* a eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite23.0ms

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:

10.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series43.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* b eps)) 1.0)
7.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (8.0ms)

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

prune145.0ms

Filtered

88 candidates to 66 candidates (25.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 49.6b

Counts

89 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.4b	(- (exp (* (+ a b) eps)) 1.0)
8.7b	(* (pow eps 2) (pow b 2))
11.3b	(* (pow eps 3) (pow b 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
22×	`prod-exp`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`associate-/r/`
6×	`cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`cube-mult` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 155

Calls

4 calls:

22.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 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))
9.0ms	(* (pow eps 3) (pow b 3))

series685.0ms

Counts

4 → 12

Calls

4 calls:

650.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
18.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	848	1789
1	5001	1488

prune347.0ms

Filtered

167 candidates to 96 candidates (42.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	170	3	173

Merged error: 0.0b

Counts

173 → 3

localize4.0ms

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))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify63.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2755	90
4	5001	90

prune38.0ms

Filtered

22 candidates to 14 candidates (36.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Merged error: 0.0b

Counts

25 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

33.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
12.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
12.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
12.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
24.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
21.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
21.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	442	1931
1	1535	1682
2	5002	1499

prune266.0ms

Filtered

171 candidates to 87 candidates (49.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

regimes161.0ms

Accuracy

0% (3.1b remaining)

Error of 3.2b against oracle of 0.1b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.7s	2583×	body	2560	valid
1.9s	3429×	body	1280	valid
362.0ms	1078×	body	640	valid
191.0ms	9932×	pre	80	true
129.0ms	1930×	body	80	overflowed
78.0ms	332×	body	320	valid
31.0ms	433×	body	80	valid
22.0ms	147×	body	160	valid

Details

sample209.0ms

simplify95.0ms

prune4.0ms

localize16.0ms

rewrite23.0ms

series43.0ms

simplify40.0ms

prune145.0ms

localize30.0ms

rewrite49.0ms

series685.0ms

simplify43.0ms

prune347.0ms

localize4.0ms

rewrite13.0ms

series3.0ms

simplify63.0ms

prune38.0ms

localize9.0ms

rewrite78.0ms

series92.0ms

simplify57.0ms

prune266.0ms

regimes161.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

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