Details

Time bar (total: 55.7s)

sample553.0ms

Algorithm
intervals
Results
165.0ms82×body2560valid
161.0ms61×body10240exit
147.0ms106×body1280valid
29.0ms35×body640valid
15.0ms317×pre80true
4.0ms7×body320valid
3.0ms19×body80valid
3.0ms7×body160valid

simplify259.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
259.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.7b

localize58.0ms

Local error

Found 4 expressions with local error:

28.6b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
15.9b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* eps b))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
8×associate-/l*
7×cbrt-undiv div-exp
6×pow1 associate-/r* div-inv
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l* prod-exp cbrt-unprod
2×clear-num frac-2neg
1×expm1-log1p pow-prod-down *-commutative expm1-udef unswap-sqr associate-/l/
Counts
4 → 108
Calls
4 calls:
Slowest
16.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
11.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
6.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* eps b))

series962.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
624.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
163.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
117.0ms
(* (expm1 (* (+ a b) eps)) eps)
58.0ms
(expm1 (* eps b))

simplify13.9s

Counts
145 → 120
Calls
145 calls:
Slowest
619.0ms
(/ (/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
589.0ms
(/ (/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
420.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
418.0ms
(* (- (exp (* (+ a b) eps)) 1) eps)
416.0ms
(* (* (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))) (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))))

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×times-frac
13×fma-def
10×add-sqr-sqrt add-cube-cbrt
7×distribute-lft-out
5×div-inv
3×add-log-exp
1×expm1-log1p-u pow1 +-commutative sum-log flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 log1p-expm1-u
Counts
1 → 35
Calls
1 calls:
Slowest
17.0ms
(+ (/ 1 a) (/ 1 b))

series19.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
19.0ms
(+ (/ 1 a) (/ 1 b))

simplify2.0s

Counts
27 → 38
Calls
27 calls:
Slowest
448.0ms
(- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))
420.0ms
(* (* (+ (/ 1 a) (/ 1 b)) (+ (/ 1 a) (/ 1 b))) (+ (/ 1 a) (/ 1 b)))
390.0ms
(+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))
343.0ms
(+ (pow (/ 1 a) 3) (pow (/ 1 b) 3))
21.0ms
(+ (/ 1 a) (/ 1 b))

prune334.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

15.7b
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
5.4b
(/ (* eps b) a)
0.0b
(expm1 (* eps b))
0.0b
(+ (/ (* eps b) a) eps)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
18×times-frac
17×add-sqr-sqrt add-cube-cbrt
11×add-cbrt-cube add-exp-log
7×fma-def
6×associate-/r* add-log-exp
5×log1p-expm1-u distribute-lft-out associate-/l*
4×expm1-log1p-u pow1 insert-posit16
3×cbrt-undiv div-exp div-inv
2×clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×+-commutative expm1-log1p sum-log prod-exp cbrt-unprod expm1-udef
Counts
4 → 94
Calls
4 calls:
Slowest
59.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
26.0ms
(+ (/ (* eps b) a) eps)
19.0ms
(/ (* eps b) a)
1.0ms
(expm1 (* eps b))

series223.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
57.0ms
(expm1 (* eps b))
51.0ms
(+ (/ (* eps b) a) eps)
31.0ms
(/ (* eps b) a)

simplify7.9s

Counts
116 → 106
Calls
116 calls:
Slowest
660.0ms
(- (+ (/ 1 b) (/ 1 a)) (* 1/2 (/ (* eps b) a)))
589.0ms
(* (* (+ (/ (* eps b) a) eps) (+ (/ (* eps b) a) eps)) (+ (/ (* eps b) a) eps))
400.0ms
(+ (pow (/ (* eps b) a) 3) (pow eps 3))
371.0ms
(* (expm1 (* eps b)) (+ (* (/ (* eps b) a) (/ (* eps b) a)) (- (* eps eps) (* (/ (* eps b) a) eps))))
351.0ms
(- (* (/ (* eps b) a) (/ (* eps b) a)) (* eps eps))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

16.3b
(cbrt (expm1 (* eps b)))
16.3b
(cbrt (expm1 (* eps b)))
16.3b
(cbrt (expm1 (* eps b)))
5.4b
(/ (* eps b) a)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac pow1/3
2×cbrt-undiv div-exp
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 66
Calls
4 calls:
Slowest
14.0ms
(/ (* eps b) a)
1.0ms
(cbrt (expm1 (* eps b)))
1.0ms
(cbrt (expm1 (* eps b)))
1.0ms
(cbrt (expm1 (* eps b)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(cbrt (expm1 (* eps b)))
123.0ms
(cbrt (expm1 (* eps b)))
117.0ms
(cbrt (expm1 (* eps b)))
35.0ms
(/ (* eps b) a)

simplify4.4s

Counts
88 → 78
Calls
88 calls:
Slowest
381.0ms
(pow (- (exp (* eps b)) 1) 1/3)
376.0ms
(pow (- (exp (* eps b)) 1) 1/3)
373.0ms
(pow (- (exp (* eps b)) 1) 1/3)
364.0ms
(pow (- (exp (* eps b)) 1) 1/3)
362.0ms
(pow (- (exp (* eps b)) 1) 1/3)

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes174.0ms

Accuracy

11% (2.9b remaining)

Error of 2.9b against oracle of 0.0b and baseline of 3.3b

bsearch632.0ms

end0.0ms

sample20.0s

Algorithm
intervals
Results
6.5s2604×body2560valid
5.8s3404×body1280valid
5.0s1978×body10240exit
1.0s1082×body640valid
503.0ms130×body160valid
481.0ms9982×pre80true
230.0ms346×body320valid
77.0ms438×body80valid