Details

sample221.0ms

Algorithm

intervals

Results

80.0ms	90×	body	2560	valid
64.0ms	64×	body	10240	exit
44.0ms	93×	body	1280	valid
8.0ms	31×	body	640	valid
5.0ms	320×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	29×	body	80	valid
0.0ms	3×	body	160	valid

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 57.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* a eps)) 1.0)
2.8b	(- (exp (* b eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite119.0ms

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:

70.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
13.0ms	(- (exp (* a eps)) 1.0)
17.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series181.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
35.0ms	(- (exp (* a eps)) 1.0)
34.0ms	(- (exp (* b eps)) 1.0)
54.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (48.0ms)

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

prune430.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 48.2b

localize22.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* eps b)) 1.0))
2.3b	(- (exp (* a eps)) 1.0)
2.8b	(- (exp (* eps b)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite120.0ms

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:

73.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* eps b)) 1.0))
14.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* eps b)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series173.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* eps b)) 1.0))
33.0ms	(- (exp (* a eps)) 1.0)
39.0ms	(- (exp (* eps b)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	481	1660
1	1985	1242
2	5003	1217

prune417.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 48.2b

localize19.0ms

Local error

Found 4 expressions with local error:

2.3b	(log (exp (- (exp (* a eps)) 1.0)))
2.3b	(- (exp (* a eps)) 1.0)
2.8b	(- (exp (* b eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
33×	`add-cube-cbrt`
14×	`log-prod`
11×	`exp-sum`
10×	`add-log-exp`
9×	`fma-neg`
6×	`log-pow`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 115

Calls

4 calls:

28.0ms	(log (exp (- (exp (* a eps)) 1.0)))
14.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* b eps)) 1.0)
19.0ms	(- (exp (* (+ a b) eps)) 1.0)

series159.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(log (exp (- (exp (* a eps)) 1.0)))
39.0ms	(- (exp (* a eps)) 1.0)
33.0ms	(- (exp (* b eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	417	1069
1	1208	735
2	5001	578

prune431.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 48.2b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (exp a) (* 2 eps))
1.0b	(* (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (- (exp (* eps b)) 1.0))
2.8b	(- (exp (* eps b)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`flip3--` `associate-r` `flip--`
4×	`expm1-log1p-u` `frac-times` `sub-neg` `pow-pow` `associate-l` `log1p-expm1-u`
3×	`unpow-prod-down` `exp-prod` `flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`
2×	`diff-log` `associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-unpow` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 129

Calls

4 calls:

5.0ms	(pow (exp a) (* 2 eps))
83.0ms	(* (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (- (exp (* eps b)) 1.0))
17.0ms	(- (exp (* eps b)) 1.0)
16.0ms	(- (exp (* (+ a b) eps)) 1.0)

series218.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (exp a) (* 2 eps))
79.0ms	(* (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (- (exp (* eps b)) 1.0))
35.0ms	(- (exp (* eps b)) 1.0)
54.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify87.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	626	1758
1	2722	1352
2	5002	1339

prune538.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 48.0b

regimes192.0ms

Accuracy

52% (5.1b remaining)

Error of 54.8b against oracle of 49.7b and baseline of 60.3b

bsearch324.0ms

Steps

Iters	Range		Point
9	3.9457466347433044e+57	2.543299118628485e+63	3.146231950313865e+60
9	-3.112004471340841e+50	-3.441044939126456e+43	-1.9491922328941345e+49

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	51
1	57	51

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.5s	2606×	body	2560	valid
1.7s	1981×	body	10240	exit
1.6s	3414×	body	1280	valid
274.0ms	1060×	body	640	valid
143.0ms	9984×	pre	80	true
62.0ms	355×	body	320	valid
22.0ms	448×	body	80	valid
13.0ms	120×	body	160	valid