Details

sample231.0ms

Algorithm

intervals

Results

87.0ms	87×	body	2560	valid
58.0ms	65×	body	10240	exit
52.0ms	110×	body	1280	valid
9.0ms	36×	body	640	valid
5.0ms	321×	pre	80	true
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	11×	body	80	valid

simplify100.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	13
5	5001	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.4b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

72.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
16.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series155.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
29.0ms	(- (exp (* b eps)) 1.0)
35.0ms	(- (exp (* a eps)) 1.0)
43.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	488	1660
1	2051	1241
2	5003	1216

prune442.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.7b

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
13.0b	(* (pow eps 2) (pow b 2))
14.7b	(* (pow eps 3) (pow b 3))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `unswap-sqr`
28×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-diff` `prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
6×	`fma-neg`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

15.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* (pow eps 2) (pow b 2))
23.0ms	(* (pow eps 3) (pow b 3))

series168.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* a eps)) 1.0)
42.0ms	(- (exp (* (+ a b) eps)) 1.0)
34.0ms	(* (pow eps 2) (pow b 2))
58.0ms	(* (pow eps 3) (pow b 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	554	1114
1	2456	873
2	5002	825

prune709.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 49.2b

localize30.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (pow eps 3) b)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
5.1b	(* (* (* (pow eps 3) b) b) (pow (cbrt b) 3))
13.0b	(* (pow eps 2) (pow b 2))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
49×	`add-sqr-sqrt`
48×	`prod-exp`
29×	`associate-r`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt` `unpow-prod-down`
21×	`associate-l`
20×	`unswap-sqr`
17×	`add-cbrt-cube`
15×	`pow-to-exp` `pow-exp`
13×	`sqr-pow`
10×	`cube-prod` `unpow2`
9×	`prod-diff`
8×	`cbrt-unprod`
6×	`cbrt-prod` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `*-commutative`
2×	`cube-mult` `unpow3`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 161

Calls

4 calls:

13.0ms	(* (pow eps 3) b)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
76.0ms	(* (* (* (pow eps 3) b) b) (pow (cbrt b) 3))
17.0ms	(* (pow eps 2) (pow b 2))

series187.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (pow eps 3) b)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)
87.0ms	(* (* (* (pow eps 3) b) b) (pow (cbrt b) 3))
30.0ms	(* (pow eps 2) (pow b 2))

simplify138.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (126.0ms)

Iter	Nodes	Cost
0	616	999
1	3374	781
2	5001	738

prune713.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 49.2b

localize34.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (pow eps 3) b)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
5.1b	(* (* (* (pow eps 3) b) b) (pow (cbrt b) 3))
13.0b	(* (pow eps 2) (pow b 2))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
49×	`add-sqr-sqrt`
48×	`prod-exp`
29×	`associate-r`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt` `unpow-prod-down`
21×	`associate-l`
20×	`unswap-sqr`
17×	`add-cbrt-cube`
15×	`pow-to-exp` `pow-exp`
13×	`sqr-pow`
10×	`cube-prod` `unpow2`
9×	`prod-diff`
8×	`cbrt-unprod`
6×	`cbrt-prod` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `*-commutative`
2×	`cube-mult` `unpow3`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 161

Calls

4 calls:

13.0ms	(* (pow eps 3) b)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
73.0ms	(* (* (* (pow eps 3) b) b) (pow (cbrt b) 3))
22.0ms	(* (pow eps 2) (pow b 2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (pow eps 3) b)
41.0ms	(- (exp (* (+ a b) eps)) 1.0)
85.0ms	(* (* (* (pow eps 3) b) b) (pow (cbrt b) 3))
33.0ms	(* (pow eps 2) (pow b 2))

simplify140.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (123.0ms)

Iter	Nodes	Cost
0	616	999
1	3374	781
2	5001	738

prune746.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 49.2b

regimes186.0ms

Accuracy

50.5% (4.2b remaining)

Error of 53.5b against oracle of 49.3b and baseline of 57.8b

bsearch309.0ms

Steps

Iters	Range		Point
7	8.712263967736246e+126	3.260842031768285e+128	9.716140837926457e+126
9	-3.889995037463458e+74	-1.693162129245245e+66	-1.9693375139914443e+72

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	43
1	66	43

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	2587×	body	2560	valid
1.8s	2040×	body	10240	exit
1.7s	3506×	body	1280	valid
272.0ms	989×	body	640	valid
151.0ms	10043×	pre	80	true
59.0ms	320×	body	320	valid
26.0ms	458×	body	80	valid
16.0ms	143×	body	160	valid